Kylliann De Santiago

Marie Szafranski

Christophe Ambroise

Mixture of stochastic block models for multiview clustering

In this work, we propose an original method for aggregating multiple clustering coming from different sources of information. Each partition is encoded by a co-membership matrix between observations. Our approach uses a mixture of Stochastic Block Models (SBM) to group co-membership matrices with similar information into components and to partition observations into different clusters, taking into account their specificities within the components. The parameters are estimated using a Variational Bayesian EM algorithm. The Bayesian framework allows for selecting an optimal numbers of clusters and components.

Multiview data and late fusion clustering

Most everyday learning situations are achieved by integrating different sources of information, such as vision, touch and hearing. A source of information in a given format will be referred to as a modality or a view. Multimodal or multiview machine learning aims to learn models from multiple views (e.g. text, sound, image, etc.) in order to represent, translate, align, fusion, or co-learn [START_REF] Baltrušaitis | Multimodal machine learning: A survey and taxonomy[END_REF][START_REF] Zhao | Multi-view learning overview: Recent progress and new challenges[END_REF].

The corresponding learning models vary based on their fusion strategy. The three main methods are early, intermediate, and late fusion of views. Late fusion is well suited to clustering since each view is often associated to dedicated efficient clustering algorithms. In this work, we are interested to build a coordinated representation of the resulting partitions through a probabilistic model. This coordinated representation should provide details about consensus and complementary information existing between the different views both at a global and local level [START_REF] Zhao | Multi-view learning overview: Recent progress and new challenges[END_REF].

Several methods have been developed to discover relationships across multiple clustering results. Consensus clustering is a family of methods which are based on the construction of a consensus matrix that represents the degree of agreement among different clustering algorithms, as in [START_REF] Monti | Consensus clustering: a resampling-based method for class discovery and visualization of gene expression microarray data[END_REF]. Tensor-based meta-clustering utilizes multilinear algebra decomposition techniques to identify patterns and relationships across each layer of this tensor ; in case of meta-clustering, all layers are often adjacency matrices, as in [START_REF] Jing | Community detection on mixture multilayer networks via regularized tensor decomposition[END_REF]. Finally, Mixture Multilayer Stochastic Block Models expands the traditional SBM by considering multilayer networks, allowing the layers to come from a mixture model, as in [START_REF] Rebafka | Model-based clustering of multiple networks with a hierarchical algorithm[END_REF].

We propose a Bayesian multilayer SBM approach, MIxture of Multiview Integrator SBM (mimi-SBM), that takes into account several sources of information, and where the membership clustering is traversing, as illustrated in Figure 1. The next section introduces notations and model, followed by synthetic experiments for comparing and evaluating the performances of the proposed approach. We conclude with a discussion section.

A mixture of stochastic block models

Performing clustering with mixture models amounts to an inference problem since the cluster labels are the model latent variables. In our context, we consider two sets of latent variables respectively corresponding to the structure of the observations and the structure of the views. We assume that the views are generated by a mixture model, in which each component is itself a stochastic block model. This allows us to capture the complex dependencies between the views, and to accurately model the underlying structure of the data.

Let A ∈ {0, 1} N ×N ×V be a tensor where N is the number of vertices (observations), and V the number of views. A is defined as a natural extension of an adjacency matrix for multiple graphs

(G 1 , • • • , G V ) with corresponding vertices A ijv = { 1, if individuals i, j are linked in G v , 0, otherwise.
The nodes and their corresponding order are the same throughout all views.

Let denote W ∈ {0, 1} V ×Q , the indicator membership matrix for the views, and Z ∈ {0, 1} N ×K , the indicator membership matrix of observations, where K is the number of view traversing clusters and Q the number of components of the view mixture. Each line of matrix W follows a multinomial distribution,

W v ∼ M(1, ρ = (ρ 1 , . . . , ρ Q )).
Although we use multiple views with their own cluster structure, we assume a traversing structure for the latent variables across all views. By leveraging all available sources of information, we aim to achieve a more comprehensive understanding of the data and obtain community structures that are consistent across all views. The individuals are thus assumed to come from a number K of sub-populations. Each latent class vector follows a multinomial distribution,

Z i ∼ M(1, π = (π 1 , . . . , π K )).
Eventually, the probability of an edge between individuals i and j on the view v, given the latent variables, is Wvs .

P(A | Z, W, Θ) = N ∏ i=1, i<j K ∏ k,l=1 V ∏ v=1 Q ∏ s=1 ( α Aijv kls (1 -α kls ) 1-Aijv ) Z ik Z jl
The proposed Bayesian model considers the following classical distributions in the context of SBM [START_REF] Latouche | Variational bayesian inference and complexity control for stochastic block models[END_REF]:

P(π | β 0 = (β 0 1 , . . . , β 0 K )) = Dir(π; β 0 ) , P(ρ | θ 0 = (θ 0 1 , . . . , θ 0 Q )) = Dir(ρ; θ 0 ) ,
where Dir(•) define the Dirichlet distribution which is the conjugate prior for the multinomial distribution. Concerning the parameters of the SBMs, we use independent Beta priors to model the connectivity matrices

P(α | η 0 = (η 0 kls ), ξ 0 = (ξ 0 kls )) = ∏ k,k<l ∏ s Beta(α kls ; η 0 kls , ξ 0 kls ) .
Jeffrey's prior seeks to establish a non-biased prior distribution for a parameter, thus reducing subjectivity in analysis [START_REF] Jeffreys | An invariant form for the prior probability in estimation problems[END_REF].

In case of a Dirichlet distribution, we have β 0 k = θ 0 s = 1/2 , ∀k, s and for Beta distribution we can choose η 0 kls = ξ 0 kls = 1/2 , ∀k, l, s too [START_REF] Latouche | Variational bayesian inference and complexity control for stochastic block models[END_REF]. The marginal likelihood of observed data is defined as

P (A) = ∑ Z ∑ W ∫ ∫ ∫ P (A, Z, W, α, π, ρ) dα dπ dρ .
Computing the marginal likelihood is a challenging problem in SBM. Integrals in the formula for the marginal likelihood are difficult or impossible to compute analytically, and sums over Z and W are often intractable as soon as the number of parameters or observations is large.

Given a variational distribution q(•) over {Z, W, α, π, ρ}, we can decompose the marginal log-likelihood into Evidence Lower BOund (ELBO) and KLdivergence between variational and posterior distribution:

log (P(A)) = L (q(•)) + KL (q(•)∥ P(• | A)) , (1)
A convenient variational distribution, often from the exponential family, is chosen. Its parameters are optimized to minimize KL-divergence.

Using the mean-field approximation, we assume that q(•) can be factorised as

q(Z, W, α, π, ρ) = N ∏ i=1 q(Z i ) V ∏ v=1 q(W v ) Q ∏ s=1 K ∏ k,k≤l
q(α kls ) q(π) q(ρ) .

(

) 2
According to ( 1) and ( 2), given a well defined distribution q(•), the ELBO is

L (q(•)) = lBeta(β) -lBeta(β 0 ) + lBeta(θ) -lBeta(θ 0 ) + K ∑ k≤l Q ∑ s=1 log ( Γ ( η 0 kls + ξ 0 kls ) Γ (η kls ) Γ (ξ kls ) Γ (η kls + ξ kls ) Γ (η 0 kls ) Γ (ξ 0 kls ) ) - N ∑ i K ∑ k τ ik log(τ ik ) - V ∑ v Q ∑ s ν vs log(ν vs ) ,
where Γ(•) is the Gamma function, lBeta(•) the log multinomial Beta function, and the estimated probabilities τ ik and ν vs are respectively related to the memberships of observation i to cluster k and view v to component s. This function is also called ILvb and can be used for model selection.

Simulation study

The Adjusted Rand Index (ARI) measures partition similarity in upcoming simulation. It quantifies agreement between model predictions and true partition, reflecting paired observations' grouping or separation. ARI near 1 signifies higher partition similarity.

For model comparison, artificial data is generated (adjacent matrices)from source mixtures and individual clustering. Various parameter values test different scenarios: N (observations), V (views), K (clusters), and Q (sources) are varied. For the other parameters, they have been set as follows : π, ρ corresponding to an equiprobability of belonging to a cluster or component, thus

{π k } K k=1 = 1/K and {ρ s } Q s=1 = 1/Q . Also, α is a tensor composed of matrices.
To have a simulation model that closely resembles a co-membership matrix, the matrices have 0.99 on the diagonal 0.01 and elsewhere. This setting strongly encourages links between individuals within the same cluster while allowing for some noise. The code for the simulations is available on GitHub in the repository mimiSBM. In Figure 2 it has been observed that mini-SBM achieved the best clustering results for each considered experimental configuration. Indeed, mini-SBM recorded the highest ARI score for all data sizes, number of clusters and sources. M3C model improved with increased factors, while TWIST struggled with complex clustering, hinting at its limited suitability for difficult problems. The second problem is the clustering of views. In Figure 3, Limited observations challenge source identification for all models. Graphclust stands out significantly, with non-overlapping boxplots compared to the other two models. As observations increase in the second simulation, model performances improve. Graphclust identifies true sources less than mimi-SBM and TWIST. TWIST mostly identifies true members but with occasional errors, seen as boxplot out-liers.

The mimi-SBM model has demonstrated a clear ability in recovering the stratification of individuals and the components of the mixture of views. However, as with any statistical model, its performance, particularly on the mixture of views, improves with larger numbers of observations. Given the importance of accurately modeling mixture components in a variety of applications, these results highlight the potential utility of mimi-SBM in a range of contexts.

Conclusive remarks

In our simulation setting, the proposed Bayesian mixture multiview SBM approach has been shown to outperform methods based on tensor decomposition, hierarchical model-based SBM, and reference model in consensus clustering.

An interesting follow-up would be to extend this approach to the context of deep learning, specifically in the context of variational auto-encoders using the Bayesian formulation. Additionally, further research is needed to develop theoretical proofs regarding the convergence of parameters for the componentconnection probability tensor model and explore the identifiability of this model.

Fig. 1 :

 1 Fig. 1: Illustration of mimi-SBM. Left: Four adjacency matrices coming from four different views which can be organized into two components. Right: identification of the two components from the views (local and complementary information) and clustering of the observations (global and consensus information).

1

 1

1Fig. 2 :

 2 Fig. 2: Boxplot of ARI measure between true individual partition and output partition of M3C [3], mimi-SBM and TWIST [4] models.

3 Fig. 3 :

 33 Fig. 3: Boxplot of ARI measure between true view clustering and output clustering of Graphclust [5], mimi-SBM and TWIST [4] models.

ESANN 2023 proceedings, European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. Bruges (Belgium) and online event, 4-6 October 2023, i6doc.com publ., ISBN 978-2-87587-088-9. Available from http://www.i6doc.com/en/.

ESANN 2023 proceedings, European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. Bruges (Belgium) and online event, 4-6 October 2023, i6doc.com publ., ISBN 978-2-87587-088-9. Available from http://www.i6doc.com/en/.


Léon Marbach
email: lmarbach@stanford.edu

Agnès Van Zanten

WITH A LITTLE HELP FROM MY FAMILY AND FRIENDS: SOCIAL CLASS AND CONTEXTUAL VARIATIONS IN THE ROLE OF PERSONAL NETWORKS IN STUDENTS' HIGHER EDUCATION PLANS

Keywords: Higher education plans, personal networks, social capital, social class, France

This article analyses the influence of family and friends on students' higher education plans. Using a Bourdieusian framework, it examines social class and contextual influences on both the structure of students' networks and the content of interactions within them. These are shown to be dependent on the dispositions and capitals of both the students and the members of those networks. Relying on data from a questionnaire circulated among 1,645 French lycée students, the article shows the existence of significant social class differences in the frequency and nature of students' interactions about higher education with various types of family members and friends. It also highlights that these differences are subject to contextual variations, with students from the same social background interacting differently with their personal networks about their higher education plans depending on the school they attend and the track in which they are enrolled.

Introduction

Despite the widespread ideal of 'college-for-all' and rising levels of enrolment in higher education (HE) [START_REF] Goyette | College for Some to College for All: Social Background, Occupational Expectations, and Educational Expectations Over Time[END_REF], different social groups still have very unequal rates of access to certain HE tracks, higher education institutions (HEIs) and fields of study [START_REF] Boliver | Expansion, Differentiation, and the Persistence of Social Class Inequalities in British Higher Education[END_REF]. A large body of sociological research has explored the different factors responsible for these social inequalities, including the role of tracks in secondary education and HE [START_REF] Duru-Bellat | Du Baccalauréat à l'Enseignement Supérieur en France: Déplacement et Recomposition des Inégalités[END_REF]Shavit et al. 2007), the rules governing national application and admissions systems [START_REF] Frouillou | Le Rôle des Instruments dans la Sélection des Bacheliers dans l'Enseignement Supérieur. La Nouvelle Gouvernance des Affectations par les Algorithmes[END_REF], and HEIs' selection criteria and procedures [START_REF] Alon | The Evolution of Class Inequality in Higher Education: Competition, Exclusion, and Adaptation[END_REF][START_REF] Zimdars | Fairness and Undergraduate Admissions: A Qualitative Exploration of Admissions Choices at the University of Oxford[END_REF]. Scholarship focusing on students has mostly emphasised the importance of the family economic and cultural capital available to young people as they prepare their HE futures [START_REF] Noble | Cultural Capital as an Explanation of Variation in Participation in Higher Education[END_REF]Reay et al. 2001b) and the role of 'institutional habitus' and guidance in secondary schools [START_REF] Olivier | Channelling Students into Higher Education in French Secondary Schools and the Re-Production of Educational Inequalities. Discourses and Devices[END_REF][START_REF] Mcdonough | Choosing Colleges: How Social Class and Schools Structure Opportunity[END_REF][START_REF] Pugsley | The University Challenge: Higher Education Markets and Social Stratification[END_REF]Reay et al. 2001a).

In this article, we focus on how personal networks influence students' HE plans. Our underlying postulate is that the structure of these networks, and the interactions that take place within them, significantly contribute to reproducing social inequalities. As we show in the next section, a large number of studies, particularly in the US, have explored the influence of both parental and friendship networks on students' HE aspirations and patterns of enrolment. We believe, however, that key dimensions have yet to be addressed. These include, in particular, the frequency of discussions with, and influence ascribed to, different types of family members and friends, the content of these discussions, and how these factors vary across social groups and school contexts. To address these gaps, we draw on responses to a questionnaire by a sample of French students attending diverse lycées [upper-secondary schools] in the Paris metropolitan region 1 . We also believe that drawing on a Bourdieusian framework can provide a better understanding of social and contextual differences in the configuration and role of personal networks.

Background

As early as the 1960s, research in the US using the 'Wisconsin model' of social mobility analysed the influence of 'significant others' (i.e. parents, peers and teachers) on students' educational and occupational aspirations and choices [START_REF] Alexander | Peer Influences on Adolescent Educational Aspirations and Attainments[END_REF][START_REF] Duncan | Peer Influences on Aspirations: A Reinterpretation[END_REF]). Many studies have underlined the importance of parental involvement in how young people develop HE aspirations and plans [START_REF] Ceja | Chicana College Aspirations and the Role of Parents: Developing Educational Resiliency[END_REF][START_REF] Hill | Social Capital for College: Network Composition and Access to Selective Institutions Among Urban High School Students[END_REF][START_REF] Perez | Understanding Latina and Latino College Choice: A Social Capital and Chain Migration Analysis[END_REF][START_REF] Perna | Differences in the Decision to Attend College Among African Americans, Hispanics, and Whites[END_REF]. This research is strongly influenced by Coleman's theorisation of 'social capital ' (1988) which emphasises the individual and collective benefits derived from close-knit social ties, in terms of social control and social support. Studies focusing on students with immigrant backgrounds have also borrowed Portes' (1998) concept of 'bounded solidarity' and, more recently, [START_REF] Yosso | Whose Culture has Capital? A Critical Race Theory Discussion of Community Cultural Wealth[END_REF] concept of 'community cultural wealth', to draw attention to the importance of high aspirations, moral support, and social skills transmitted to these students through family and kin networks [START_REF] Luedke | Lifting While We Climb: Undergraduate Students of Color Communal Uplift and Promotion of College-Going Within their Communities[END_REF][START_REF] Gao | Exploring the Role of Community Cultural Wealth in University Access for Minority Students[END_REF].

Several of these studies have nevertheless emphasised that it is crucial for these students to receive institutional support in order to access the opportunities and resources afforded to other students by their family networks [START_REF] Stanton-Salazar | Social Capital and the Reproduction of Inequality: Information Networks among Mexican-Origin High School Students[END_REF][START_REF] Perna | The Relationship Between Parental Involvement as Social Capital and College Enrollment: An Examination of Racial/Ethnic Group Differences[END_REF][START_REF] Fann | Parent Involvement in the College Planning Process: A Case Study of P-20 Collaboration[END_REF].

There is also a substantial body of literature on the role of students' peers and friends. Some of the initial studies in this area examined the relative influence of parents and peers, and generally concluded that parents have the most decisive impact on students' HE aspirations [START_REF] Kandel | Parental and Peer Influences on Educational Plans of Adolescents[END_REF]. Others only explored the role of friends and the degree to which similar educational aspirations reflect homophilic tendencies in friendships with respect to social background, ambition or interpersonal pressures to conform [START_REF] Duncan | Peer Influences on Aspirations: A Reinterpretation[END_REF]). A different set of studies focused on peers as part of a more general interest in secondary school effects on university intentions [START_REF] Alwin | High School Context Effects on Aspirations[END_REF][START_REF] Meyer | High School Effects on College Intentions[END_REF]. This research highlights that peers have a noteworthy influence on low-income, urban and minority secondary-school students' HE plans [START_REF] Fletcher | High School Climate and College Success[END_REF]. In many cases, peers act as effective role models and sources of relevant information and advice, while also providing emotional support [START_REF] Stanton-Salazar | A Social Capital Framework for Understanding the Socialization of Racial Minority Children and Youth[END_REF], especially when they adopt the formal role of 'peer counselor' [START_REF] Tierney | Fictive Kin and Social Capital: The Role of Peer Groups in Applying and Paying for College[END_REF]. In other cases, though, they provide poor examples of academic engagement or incomplete or questionable advice and information [START_REF] Holland | The Power of Peers: Influences on Postsecondary Education Planning and Experiences of African American Students[END_REF]).

In the UK, several studies have highlighted the importance of students' personal networks on their HE plans and choices [START_REF] David | Gender Issues in Parental Involvement in Student Choices of Higher Education[END_REF][START_REF] Pugsley | The University Challenge: Higher Education Markets and Social Stratification[END_REF]). In particular, Rachel Brooks ' (2003, 2004) qualitative study, which explored both parental and peer influences on a group of secondary school students from lower-middle class families emphasised the significant involvement of fathers in the decision-making process and the complementary role of students' parents and friends, with the former informing their general understanding of the HE market and the latter exerting a greater influence on the choice of institutions and courses.

In continental Europe, there has been even more limited interest in this topic, with only a handful of studies focusing on the role of parents and peers in transition to HE. Among them, the statistical studies by [START_REF] Nakhili | Impact du Contexte Scolaire dans l'Elaboration des Choix d'Etudes Supérieures des Elèves de Terminale[END_REF] in France and [START_REF] Dupriez | Etudier à l'Université. Le Poids des Pairs et du Capital Culturel Face aux Aspirations d'Etudes[END_REF] in francophone Belgium found contextual effects on HE choices related to peers' social background and academic level, while [START_REF] Van Houtte | School Ethnic Composition and Aspirations of Immigrant Students in Belgium[END_REF], working in Flemish Belgium, concluded that immigrant students in secondary schools with a high concentration of similar peers had slightly higher HE aspirations. [START_REF] Orange | Le BTS et la Gestion des Aspirations Scolaires[END_REF] qualitative study in France showed, on the other hand, the impact of peer norms and pressures on working-class students' choices of vocational HE tracks. These results align with those of recent research on Sweden and Denmark focusing on peer influence in the choice of upper-secondary tracks [START_REF] Rosenqvist | Two Functions of Peer Influence on Upper-Secondary Application Behavior[END_REF][START_REF] Smith | Peer Preferences and Educational Decisions. Heterogeneous Associations Across Student Socioeconomic Status[END_REF].

Conceptual framework

In this article, we adopt a Bourdieusian perspective on the role of students' personal networks in influencing their HE plans. This has three major implications. The first is that we focus on networks as organically related to actors' positions in the social space. This in turn implies, first, that actors' engagement with networks is influenced by their membership of a group of individuals sharing similar living conditions and corresponding sets of habitus, or configurations of dispositions, that is values, worldviews, and practices acquired through socialisation. Second, it implies that the influence of connections, viewed as social capital, is strongly dependent on economic and cultural capital (the two other types of capital that define social groups according to Bourdieu) and can in turn modify the quantity or qualitative composition of the latter. While there is a common consensus that economic capital refers to wealth and income, there is less agreement on how to define cultural capital. Here, we adopt [START_REF] Lareau | Cultural Capital in Educational Research: A Critical Assessment[END_REF] comprehensive definition which includes not only credentials, knowledge, skills and embodied manners, and tastes and lifestyles, but also individuals' ability to comply with the expectations and evaluation standards of institutions such as schools and HEIs. We are particularly interested in the two-way relationship between cultural and social capital, that is how different volumes and types of cultural capital across social class affect interactions with members of personal networks and if and how these interactions, in turn, alter cultural resources. We will, however, also consider two further forms of social division alongside class, namely students' gender and immigrant background, as potential sources of differentiation in the composition and role of networks.

A second major implication of our Bourdieusian lens is that we focus on networks as crucial to the reproduction of prevailing class, power, and status relationships [START_REF] Bourdieu | Le capital social[END_REF][START_REF] Bourdieu | Distinction: A Social Critique of the Judgment of Taste[END_REF][START_REF] Bourdieu | The Forms of Capital[END_REF]. We consider that while all individuals and social groups rely on social ties to achieve individual and collective goals, there is a difference between viewing these ties as facilitators -or 'power to', which corresponds to Coleman's perspective, and viewing them, from Bourdieu's perspective, as sources of social profit and influence -or 'power over' [START_REF] Smith | It May Be Social but Why Is It Capital? The Social Construction of Social Capital and the Politics of Language[END_REF]. In line with Lareau and colleagues' analyses [START_REF] Lamont | Cultural Capital: Allusions, Gaps and Glissandos in Recent Theoretical Developments[END_REF][START_REF] Lareau | Moments of Social Inclusion and Exclusion: Race, Class, and Cultural Capital in Family-School Relationships[END_REF], we consider that, similarly to cultural dimensions which are not perceived and acknowledged as cultural capital in the educational field, not all types of social ties and their associated resources are equally rewarded by secondary schools and HEIs, and that only those that are directly recognised in these contexts should be called 'social capital' [START_REF] Horvat | From Social Ties to Social Capital: Class Differences in the Relations between Schools and Parent Networks[END_REF]. While our data does not allow us to empirically establish the unequal efficacy of various network configurations, we will emphasise those dimensions that have been associated in the literature with inequalities in access to HE, particularly to the most selective tracks.

A third implication of our approach concerns our perspective on contextual variations.

Setting aside the considerable inequalities that exist between secondary schools when it comes to students' chances of acquiring additional resources through interactions with school staff [START_REF] Olivier | Channelling Students into Higher Education in French Secondary Schools and the Re-Production of Educational Inequalities. Discourses and Devices[END_REF], we focus exclusively here on interactions with peers. We expect that, due to the predominance of class-based segregation in schools, the social homogeneity of peer networks will generally reinforce students' initial habitus developed through class-based primary socialization experiences. We also anticipate that, due to these segregation patterns, students will only increase their social capital, as we define it here, in schools with a concentration of upper-class students endowed with large volumes of economic and cultural capital. However, since levels of segregation vary, leaving room, even in homogeneous schools, for some degree of social mix, we are also interested in observing the structure and role of students' networks in heterogeneous schools as well as the degree to which these might modify students' initial class-based habitus when they are part of a minority surrounded by peers from contrasting social backgrounds. From a Bourdieusian perspective that also incorporates, to some degree, [START_REF] Lahire | The Plural Actor[END_REF] emphasis on the fact that in differentiated societies individuals are increasingly exposed to heterogeneous principles of socialisation, we expect these changes frequently to be incremental, tending to develop rather than fundamentally alter students' dispositions, but also sometimes, under certain conditions, to be quite radical.

Data and methods

We rely on data from a questionnaire circulated in 2015 and 2016 among French lycée students in their last year of secondary education. Our total sample comprises 1,705 students but we focus here on the vast majority (N=1,645) who stated they intended to continue to HE.

The respondents come from eight lycées, chosen to represent the diversity of upper-secondary schools in the Paris metropolitan region based on schools' administrative status (public or private), track provision (especially the presence or absence of technological and vocational tracks) and, most importantly, students' social class. In each lycée, the research team distributed the survey in the different classes under the supervision of a teacher, who made sure all students responded.

The objective of the questionnaire was to study the main influences on students' HE choices. It was carried out during the period (January-March) when students had to list and rank their HE choices on Admissions Post-Bac (APB), 2 France's national HE application and admissions platform. It included sections on the influence of family and friends, as well as of school staff, on the personal steps students had taken to inform their choices (e.g. attending university fairs or open days, reading brochures, or searching on the Internet), on their HE projects in terms of years of study and HE tracks and professional plans, as well as on their profiles. The survey questions were devised by the research team and designed to be answered in one hour.

For the present analysis, we focus on the close-ended questions about students' personal networks. The respondents were asked about their discussions about HE plans with family and friends, in terms of frequency (at least once a week/a few times/once/never) and content (we proposed 12 topics shown in Table 2). The respondents had to state whether they received opinions and/or advice during these discussions (yes/no) and, if so, whether they took them into account (yes/no). They were also prompted to mention whether someone in their personal circle was pursuing or had pursued the same HE studies they were considering. Concerning family members, questions distinguished between mothers, fathers, siblings and members of the extended family, and, concerning peers, between classmates, school friends and friends outside school.

The data were analysed using the chi-square test at a 95% level of significance on the different categorical variables. The chi-square test compares the observed frequencies in the sample with the expected frequencies if there was no relationship between the variables.

Social classes

Based on the conclusions of French research on access to HE (Duru-Bellat and Kieffer 2008) and as a result of our own theoretical focus, we consider social class as the most important variable. We constructed this variable, based on students' answers about both their parents' occupations, in several steps. First, we recoded each parent's occupation into Lower-class (LC), Middle-class (MC), Upper-class (UC) or Unemployed/undetermined using the French Institute of Statistics and Economic Studies (INSEE) classification of occupations. 3 We then distinguished seven subtypes of parental couples according to all possible combinations of these four groups. Finally, to limit the number of categories and to have enough respondents in each, we combined subtypes (see Figure 1). In what follows, we will mostly consider the three larger groups (LC, MC and UC) and refer to subtypes only in the rare cases where the responses of their members differ.

[Insert Figure 1 here]

Schools

The existing literature on school effects has shown that the social composition of the school has more impact on students' HE plans and patterns of enrolment than other characteristics [START_REF] Alwin | High School Context Effects on Aspirations[END_REF][START_REF] Meyer | High School Effects on College Intentions[END_REF]. We therefore focus particularly on this aspect, distinguishing between three types of schools: 'privileged' (when more than 70% of students' parents, including those who did not participate in the survey, are UC), 'underprivileged' (when more than 40% are LC) and 'heterogeneous' in other cases.

Social class differences in the configuration and declared influence of personal networks

As expected by our theoretical model, our results show significant differences across social classes concerning students' interactions with their personal networks. In what follows, we first examine differences in network structure, considering the relative importance of family and friends but also finer distinctions. A more qualitative perspective on the relative importance of the different members of students' personal circles is also provided by focusing on the extent to which, according to our respondents, these members express opinions and/or give advice and teaching [START_REF] Seibel | Les liens entre Pierre Bourdieu et les statisticiens à partir de son expérience algérienne[END_REF])) distinguishes six main categories among the active population: 1-Farmers (Agriculteurs exploitants); 2-Craft workers, retailers and company directors (Artisans, commerçants et chefs d'entreprise); 3-Executives and members of intellectual high-status professions (Cadres et professions intellectuelles supérieures); 4-Intermediate occupations (Professions intermédiaires); 5-Employees (Employés); 6-Blue-collar workers (Ouvriers). It is common in the French sociological literature to equate category 3 with the upper class, 1, 2 and 4 with the middle class, and 5 and 6 with the lower class.

whether these are taken into account. We then explore the content of these interactions, focusing on the relative frequency of different topics.

Social class differences in the relative importance of discussion partners

[Insert Table 1 here] LC students. Mothers are clearly the most important figure for LC students, not only in terms of frequency of interactions but also in terms of opinions and advice both given and taken into account. Comparatively, fathers are much less present -one in four students have never discussed their HE choices with them -but when they do express an opinion or give advice, they are as influential as mothers. As regards siblings, LC students do not talk more with them 4 than students from the two other social classes, and do not receive much advice from them but do tend to follow it when it is given. Moreover, siblings probably act as 'role models', since one in four students cite them when asked about people who have pursued or are pursuing the same HE course they are considering. Members of the extended family are those with whom LC students talk the least and whose opinions and advice they follow the least, although they are cited even more than siblings as people who have pursued the same studies. Friends, both inside and outside school, are important discussion partners too, respectively ranking second and third after mothers, but their opinions and advice are considered much less than those of family members. This finding is consistent with several studies comparing the relative influence of family and friends, which have found stronger parental influence on HE choices [START_REF] Davies | Parental and Peer Influences on Adolescents' Educational Plans: Some Further Evidence[END_REF] although it is also important to underline the role of older siblings in lower-class families (Uvaag 2023), since their cultural capital -in terms of familiarity with the secondary and HE systems, for those who pursued postsecondary education -can partly compensate their parents' lack of such capital [START_REF] Beaud | La France des Belhoumi[END_REF]).

4 For this item, we only consider students who stated they had at least one brother or sister.

MC students. Mothers remain central in discussions about HE but fathers play a greater role than for LC students: three out of four MC students have discussed their HE choices with their fathers several times, and very often followed their advice. This is particularly the case for subtype 3 students, probably because fathers hold the UC position in 81% of these parental couples, highlighting the importance of social class dominance effects within couples [START_REF] Jayet | When Lines of Class Division Run Through Families: Comparing Mother's and Father's Influence on Social Destiny[END_REF]. As in the case of LC students, siblings are not important discussion partners, even though one out of four MC students cite them as someone who has pursued the studies they are considering. Moreover, MC students are those who discuss HE the least with extended family members and receive the least advice from them. Friends, especially those at school, are frequent discussion partners but, as for LC students, their opinions and advice seem to count much less than those of family members.

UC students. Both parents are key discussion partners. Not only is the discrepancy between levels of discussion with mothers and fathers much smaller than in the other social groups but also fathers frequently serve as 'role models': among those UC students who state that they know someone who has followed the same HE course as the one they are considering, fathers are cited twice as much as mothers, while LC and MC students cite both equally.

Siblings play a weaker role, probably due to strong parental involvement in HE choices but also to the fact that both parents and teachers [START_REF] Olivier | Channelling Students into Higher Education in French Secondary Schools and the Re-Production of Educational Inequalities. Discourses and Devices[END_REF][START_REF] Mcdonough | Choosing Colleges: How Social Class and Schools Structure Opportunity[END_REF]Reay et al. 2001a) strongly encourage UC students to look for HE pathways that are tailored to their academic level as well as their specific personality and tastes [START_REF] Lareau | Home Advantage. Social Class and Parental Intervention in Elementary Education[END_REF]. Conversely, extended family members seem to complement parental contributions as 75% of UC students state that they take their opinions and advice into consideration. This is consistent with a Bourdieusian perspective on the role of (family) social capital among the upper classes [START_REF] Lenoir | Capital Social et Habitus Mondain. Formes et États du Capital Social dans l'Oeuvre de Pierre Bourdieu[END_REF][START_REF] Pinçon | Sociologie de la Bourgeoisie[END_REF]. Classmates and friends, especially those at school, are more important influences than in the other two social groups, not only because of the higher percentage of UC students who talk to them about their HE plans but also because their opinions and advice are frequently followed. This is related to the fact that UC students, thanks to their parents' residential and school choices strongly guided by the aim to mix with 'people like them' so as to reinforce and extend their social and cultural capital [START_REF] Ball | Class Strategies and the Education Market. The Middle Classes and Social Advantage[END_REF][START_REF] Van Zanten | Choisir son École. Stratégies Familiales et Médiations Locales[END_REF] generally attend secondary schools with students from similar social backgrounds and with similar HE projects, a subject we address in more detail below.

Social class differences in the content of discussions

[Insert Table 2 here] Overall, regardless of social class, the topics students discuss most often with family and friends are possible tracks and/or fields of study in HE, the HEIs that offer these, and the use of the APB platform. 5 Other topics prove more distinctive, reflecting different areas of concern among the three social groups.

LC students. The proportion that mention each of the topics suggested is generally lower than in the other two groups, except regarding cost and funding schemes and employment opportunities upon graduation. Their discussions also revolve less around 'strategic' topics, namely: access (e.g. chances of admission depending on academic level, selection criteria); success (e.g. content of tracks and/or fields of study, expectations of HE teaching staff and study methods); and the match between the courses envisaged and students' personality or tastes. Unsurprisingly, these responses reveal the weight of financial risks for students from families with low levels of economic capital [START_REF] Archer | Bettering Yourself?' Discourses of Risk, Cost and Benefit in Ethnically Diverse, Young Working-Class Non-Participants' Constructions of Higher Education[END_REF][START_REF] Perna | The Relationship Between Parental Involvement as Social Capital and College Enrollment: An Examination of Racial/Ethnic Group Differences[END_REF]. They also show how low levels of cultural and social capital -the latter crucially also translating into a lack of role models in their personal circles -reduces these students' capacity to consider factors crucial to their future HE careers and to develop relevant frames with which 5 The way the survey question was framed means we cannot distinguish which topics students discussed with whom but can only examine which topics received the most attention in interactions with members of their personal network in general.

to compare tracks and institutions [START_REF] Archer | Higher Education and Social Class. Issues of Exclusion and Inclusion[END_REF][START_REF] Ball | Choice, Pathways and Transitions Post-16[END_REF][START_REF] Pugsley | The University Challenge: Higher Education Markets and Social Stratification[END_REF][START_REF] Waithaka | Family Capital: Conceptual Model to Unpack the Intergenerational Transfer of Advantage in Transitions to Adulthood[END_REF][START_REF] Holland | Framing the Search: How First-Generation Students Evaluate Colleges[END_REF]. Moreover, the reduced number of topics they discuss is probably compounded by fears of not succeeding in the baccalauréat, of being rejected by selective HEIs and tracks, and of having to adapt to the unknown territory of HE [START_REF] Hugrée | L'Université qui Vient[END_REF].

MC students. These students appear closer to their LC than to their UC counterparts, especially with respect to the relative weight of financial concerns, although a higher percentage discuss other topics (e.g. HEIs' rankings, HEIs' selection criteria, and chances of success) with their personal circle. Given that they come from families with 'average' levels of economic, cultural and social capital, MC students adopt a more informed, pragmatic perspective than students whose parents are blue-collar workers and employees, prioritising HE studies that are not too costly and lead to well-paid jobs but focusing also on their chances of access and success. However, this perspective remains less 'strategic' than that of UC students and also seems to lead these students to attach less importance to how suited their HE choices are to their personality and tastes [START_REF] Brooks | Young People's Higher Education Choices: The Role of Family and Friends[END_REF].

UC students. Compared to LC and MC students, UC students talk significantly less about cost and funding schemes. While a similarly high proportion as in the other social classes mention employment opportunities after graduation, this topic, which is of primary importance for other social classes, is overall one of those they discuss least. It should be noted that these differences are mainly due to subtype 6 students, whose families probably have higher levels of economic capital than those of subtype 5. Nevertheless, our results show that UC students who, in general, face fewer financial constraints and benefit from their parents' cultural capital, are able fully to imagine HE futures for themselves combining an instrumental and an expressive perspective: on the one hand, they carefully consider the prestige and selection criteria of tracks and HEIs, as well as the best ways to use the APB platform to their advantage; on the other, they view HE as an experience of 'self-discovery' and focus on finding studies suited to their personality and tastes, as well as on the content of the courses and the expectations of HE teaching staff [START_REF] Bathmaker | Higher Education, Social Class and Social Mobility: The Degree Generation[END_REF]Reay et al. 2001b).

Intra-class variations

We also found some significant intra-class variations. Gender influences the role of family networks, with girls seeking/receiving more information and support from parents, siblings and extended family members than boys. This probably reflects the fact that girls plan their studies more seriously and express more doubts about their HE futures [START_REF] Klevan | Why the Boys are Missing. Using Social Capital to Explain Gender Differences in College Enrollment for Public High School Students[END_REF]. It is only true for LC and MC students, however, as, in line with research showing that UC parents tend to provide boys and girls with a similar 'sense of entitlement' and similar levels of confidence [START_REF] Lareau | Unequal Childhoods[END_REF], we find that female and male UC students interact to the same degree with their family members. This does not mean that these students are not socialised into different gender roles, though. In fact, such socialisation is visible in the different degrees to which, and ways in which, mothers and fathers are influential as role models [START_REF] David | Gender Issues in Parental Involvement in Student Choices of Higher Education[END_REF]): 39% of UC boys cite fathers as examples of someone who has pursued the tracks or fields of study they are considering, while only 22% of girls do so; mothers have less influence in this domain but more on girls' than on boys' study plans (22 % of girls cite their mother as an example but only 12% of boys).

We also found some differences among LC students according to immigrant background. 6 Unsurprisingly, students with two non-French parents appear, on the one hand, more disadvantaged in terms of family social capital than students with one or two French parents, as they declare fewer discussions with family members about their HE plans. On the other hand, they seem more ambitious, confirming previous studies focusing on immigrant students' aspirations [START_REF] Ichou | Les Enfants d'Immigrés à l'Ecole: Inégalités Scolaires du Primaire à l'Enseignement Supérieur[END_REF][START_REF] Modood | Capitals, Ethnicity and Higher Education[END_REF]. They also discuss a greater range of topics, especially 'strategic' ones, with their personal networks and appear less concerned about cost and employment opportunities.

For all social classes, we also observed a strong correlation between students' level of aspiration in terms of the number of years' HE they plan to complete and their interactions with their personal networks. In general, the higher their ambitions, the more interactions they have with family and friends, the more feedback they receive from them and the richer the content of these interactions -in terms of the number of topics mentioned but also the frequency of those relating to developing strategies vis-à-vis APB and HEIs and to the match between HE provision and students' expressive habitus. Frequency of interactions, especially with family members, seems to have a greater effect on aspiration levels for LC and UC students than for MC students. However, given the nature of our data, we cannot disentangle cause and effect: does ambition affect students' propensity to discuss HE with their friends and family and to focus on certain questions (or their circle's propensity to talk to them)? Or, in line with many studies on students' aspirations [START_REF] Davies | Parental and Peer Influences on Adolescents' Educational Plans: Some Further Evidence[END_REF][START_REF] Spenner | Achievement Ambitions[END_REF], do higher levels of interaction with family and friends contribute to raising students' levels of ambition? The answer is probably both.

A similar but less clear-cut pattern was also apparent regarding students' self-reported academic level, which is unsurprising given the strong correlation between this variable and students' level of aspiration. Students who view themselves as 'below average' compared to their classmates tend to talk less and about fewer topics with their personal networks. These effects are, however, more pronounced among LC and MC students, which suggests that UC students and their parents are less likely to get discouraged about making HE plans when the former are less successful [START_REF] Van Zanten | Choisir son École. Stratégies Familiales et Médiations Locales[END_REF][START_REF] Ball | Class Strategies and the Education Market. The Middle Classes and Social Advantage[END_REF]. However, it is also important to point out that, in all social classes, those students who see themselves as being 'top of their class' do not always talk more or about more topics, probably because their high grades give them more confidence to make autonomous plans [START_REF] Edwards | A Typology of Parental Involvement in Education Centring on Children and Young People: Negotiating Familialisation, Institutionalisation and Individualisation[END_REF] and/or because they receive more information and advice from teachers.

Social-class differences associated with contextual variations

The influence of social class on students' personal networks and on their role in preparing HE plans is nevertheless mediated by contextual configurations. We consider two of these in this section, namely baccalauréat track and type of secondary school, in terms of social make-up. 7 We show that these configurations significantly affect students' interactions with their personal network, particularly when they are in tracks or schools that are less common for their social group. [START_REF] Buchmann | Interpersonal Influences and Educational Aspirations in 12 Countries: The Importance of Institutional Context[END_REF] comparative study clearly shows that the influence of parents and peers on students' aspirations is much higher in relatively undifferentiated secondary school systems than in systems where students are allocated to tracks, since in the latter students are both channelled and self-selected into the HE tracks for which they are being prepared [START_REF] Meyer | High School Effects on College Intentions[END_REF]. However, this applies in particular to systems with early betweenschool tracking and has probably become less pronounced with the dramatic rise in students' expectations and enrolments in HE [START_REF] Goyette | College for Some to College for All: Social Background, Occupational Expectations, and Educational Expectations Over Time[END_REF]). In the French case, where students are separated into three major tracks (academic, technological and vocational) at the end of lower secondary school (collège) and where there has been a significant increase in the number of students continuing to HE, a more complex picture emerges from our observations with the level of interaction varying across tracks for students from similar social class backgrounds.

Variations according to lycée tracks

Our data does not, however, allow us to explore the extent to which this variation is due to a track composition effect or to strong differences between the curricula and guidance practices in each track.

LC students. LC students enrolled in vocational tracks where the great majority of students come from similar LC backgrounds, talk less about their HE choices with their siblings and friends at school, and more with friends outside school whose advice they tend to follow but not necessarily where professional opportunities are concerned -they discuss this topic less than LC students in other tracks, probably because they have a negative view of their professional futures. Those enrolled in technological tracks are more likely to have never discussed their HE choices with their mother, father or extended family members; however, school friends, either from a similar LC background but also potentially MC students given that both social groups are represented in these tracks, seem to play an important prescriptive role. This is consistent with the findings of studies showing that the social influence of friends might be stronger in heterogeneous tracks that allow for diverse future educational paths [START_REF] Lorenz | Social Influence or Selection? Peer Effects on the Development of Adolescents' Educational Expectations in Germany[END_REF]. These LC students are nevertheless also the least likely to talk to their personal networks about chances of success based on lycée grades, most likely because these are less important in the short vocational HE routes or non-selective university tracks to which most of them plan to apply [START_REF] Convert | Des Hiérarchies Maintenues. Espace des Disciplines, Morphologie de l'Offre Scolaire et Choix d'Orientation en France, 1987-2001[END_REF][START_REF] Orange | Le BTS et la Gestion des Aspirations Scolaires[END_REF]. On the other hand, LC students enrolled in academic tracks behave more like the MC and UC students they are likely to encounter in these tracks: they discuss their HE plans more frequently with family members and receive more advice from them. They are also the most likely to know someone personally who has pursued or is pursuing the studies they are considering. These students still consider cost an important topic but talk frequently about the fit between HE tracks and fields and their personality and tastes, which is a typical topic of discussion among UC students.

MC students. The track followed generates even more pronounced differences in HE discussions with personal networks among MC students.8 Those in the academic track talk significantly more about their HE projects with their mothers, fathers and extended family members, as well as with their friends inside and outside school. The number of topics discussed also increases, with a higher proportion of them citing 'strategic' ones, as well as the expectations of HE teaching staff, the content of different tracks and fields of study, and the fit between them and their personality and tastes.

UC students. These students were almost all in the academic track and we found only small differences between the three subtracks (scientific, economic and social, and literary)9 in which they complete their last two years of secondary education. The most significant difference is that those in scientific tracks receive more opinions and advice from their fathers and know more people in their personal networks (notably fathers, siblings and extended family members) who have pursued the same studies they are considering. This is partly due to the higher proportion of boys in this subtrack compared to the other two but also to the fact that it is the most selective and prestigious, viewed, as in other countries, as the 'royal road' [START_REF] Lidegran | The Royal Road of Schooling in Sweden: The Relationship between the Natural Science Programme in Upper Secondary School and Higher Education[END_REF] to high-status HE tracks and professions.

Variations according to secondary schools

Several studies have shown substantial differences in students' HE plans and choices according to the secondary school they attend [START_REF] Mcdonough | Choosing Colleges: How Social Class and Schools Structure Opportunity[END_REF][START_REF] Pugsley | The University Challenge: Higher Education Markets and Social Stratification[END_REF]Reay et al. 2001a). The three types of schools that we consider in this study, that is 'privileged', 'heterogeneous' and 'underprivileged', differ first and foremost in terms of the student population's dominant social background, which reflects the combined effect of school location and of students' and parents' choices.10 . Although, in theory, all schools must follow the same national curriculum for each track, in practice they implement different informal 'charters' [START_REF] Meyer | High School Effects on College Intentions[END_REF] depending on students' social and academic profiles, as well as their probable academic and professional futures, which influence teaching content but also HE guidance.

[Insert Table 3 here] LC students. Attending a privileged lycée has a very significant impact on LC students' interactions with their personal networks. While the small proportion of students in this situation discuss HE more with their families, especially their fathers, they receive less familial advice and have a lower tendency to follow it than LC students in other types of schools. This is strongly related to the fact that, in this context, LC students rely substantially more on their peers whose advice and opinions play a central role in their HE plans. Conversely, we observe a significant drop in the proportion of students reporting having received opinions or advice from friends outside school. There is also a strong 'contamination effect' from classmates and school friends regarding the topics discussed. While these students still worry about costs, they discuss 'strategic' topics much more frequently with their personal networks. These significant differences in LC students' habitus -which, as discussed above, were also observable among the most ambitious and academically able LC students who are those more likely to be found in these schools -are very probably also due to being exposed to a HE-oriented curriculum and to earlier, more intense and more personalised HE guidance practices from educational professionals in these settings [START_REF] Olivier | Channelling Students into Higher Education in French Secondary Schools and the Re-Production of Educational Inequalities. Discourses and Devices[END_REF][START_REF] Jack | The Privileged Poor. How Elite Colleges are Failing Disadvantaged Students[END_REF]). On the other hand, we find that attending a heterogeneous lycée has rather a negative impact on LC students, since it is in this context that they talk the least about various topics and have the fewest interactions with friends at school. This may be, firstly, because in these schools, students make very diverse HE choices, which makes it harder for them to 'get through' the process with the help of peers, and secondly, because they receive less HE guidance from school professionals.

MC students. As with LC students, we find a positive impact on discussions with personal networks for MC students when they attend a privileged school, with a strong increase in conversations with extended family members but also with school friends. However, contrary to what we observed for LC students, we do not find a decrease in the level of familial advice or students' tendency to follow it. This is probably related to the fact that, since they come from families where parents' have higher levels of cultural and social capital, these students are less likely than their LC counterparts to feel the need to turn to their upper-class school friends as compensatory sources of information and advice.

UC students. Given the small number of UC students in underprivileged schools, our comparison only concerns those in heterogeneous and privileged lycées. We find few variations in the frequency of discussions with family and friends although those in privileged lycées have a higher tendency to follow their school friends' opinions and advice. Attending a privileged rather than a heterogeneous school has stronger effects on the content of discussions: while 53% of UC students in heterogeneous schools talk about costs and funding schemes with their personal networks, only 34% do so in privileged schools. Also, while 67% of UC students in heterogeneous schools talk about institution rankings with their personal networks, 87% do so in privileged schools. These results show, on the one hand, that UC students continue to get substantial advice and support from their parents independently of the school they attend [START_REF] Lareau | Class and the Transition to Adulthood[END_REF] but also, on the other hand, that their HE plans are still conditioned by school contexts. This is probably a result of both 'selection effects', as UC students in heterogeneous schools are more likely to come from less wealthy families and to have lower academic results, and contextual effects, related to the characteristics of the peers and professionals with whom they interact.

Discussion

Coherent patterns emerge from both our analysis of social class differences in the structure of students' personal networks and the role these play in helping them develop their HE plans, and our examination of mediating contextual factors. UC students' interactions with members of their personal networks are clearly part of a more general 'Matthew effect'11 concerning the accumulation of advantages among dominant class groups [START_REF] Bourdieu | The Forms of Capital[END_REF][START_REF] Bourdieu | Reproduction in Education[END_REF]. For these students, the HE choice process is a 'family affair' [START_REF] Van Zanten | A Family Affair: Reproducing Elite Positions and Preserving the Ideals of Meritocratic Competition and Youth Autonomy[END_REF][START_REF] Lareau | Class and the Transition to Adulthood[END_REF]. They benefit from interactions with mothers who, acting both as 'mentors' and as 'strategists' [START_REF] Croll | Families, Social Capital and Educational Outcomes[END_REF], contribute in a myriad of ways to their school success and careers [START_REF] Van Zanten | Choisir son École. Stratégies Familiales et Médiations Locales[END_REF][START_REF] Edwards | A Typology of Parental Involvement in Education Centring on Children and Young People: Negotiating Familialisation, Institutionalisation and Individualisation[END_REF][START_REF] Lareau | Unequal Childhoods[END_REF], including during access to, and completion of, HE [START_REF] Armstrong | Paying for the Party. How College Maintains Inequality[END_REF]. But they also benefit from interactions with fathers and extended family members who act as role models, especially for boys [START_REF] David | Gender Issues in Parental Involvement in Student Choices of Higher Education[END_REF]. UC students further accumulate social capital for HE [START_REF] Hill | Social Capital for College: Network Composition and Access to Selective Institutions Among Urban High School Students[END_REF] from friendship networks which are probably highly homophilic given parents' efforts to encourage them to spend time with others like them [START_REF] Van Zanten | Choisir son École. Stratégies Familiales et Médiations Locales[END_REF][START_REF] Ball | Class Strategies and the Education Market. The Middle Classes and Social Advantage[END_REF]. Friends are thus able to provide information and advice that do not contradict those offered by family members but most probably complement them with up-to-date and detailed information about tracks, HEIs' rankings and selection procedures. The combined influence of parents and friends contributes to the great homogeneity of these students' choices in terms of the prestige of the tracks and HEIs to which they turn [START_REF] Albouy | Les Inégalités Sociales d'Accès aux Grandes Ecoles[END_REF]Reay et al. 2001b). It is also important to note that these students' engagement with their personal networks does not vary as much as in the other groups according to personal ambition and achievement or to the tracks and schools in which they are enrolled, probably because parental control and support limit the degree of individual and contextual variation.

At the other end of the social hierarchy, LC students' engagement with personal networks does not generally allow them to reduce their initial disadvantage vis-à-vis the other two social groups. These students have frequent discussions about HE with their families, especially with their mothers, and with both school and out-of-school friends, but presumably mostly to obtain much-needed emotional and moral support given the risks they face in HE [START_REF] David | Gender Issues in Parental Involvement in Student Choices of Higher Education[END_REF]. Although siblings and members of the extended family can act as role models and provide some degree of 'community cultural wealth' [START_REF] Yosso | Whose Culture has Capital? A Critical Race Theory Discussion of Community Cultural Wealth[END_REF], the information and advice that these students ask for and/or receive from their personal networks is mostly of a 'generic' kind [START_REF] Lareau | Home Advantage. Social Class and Parental Intervention in Elementary Education[END_REF]. It does not help them interact strategically with the national application and admissions platform or with HEIs nor does it increase their chances of finding a good fit between their aspirations, academic level and tastes and the different types of HE provision. LC girls, students with an immigrant background and academically very able students are more likely to seek out, and benefit from, the example of, and the information and advice provided by, classmates and school friends. This confirms the findings of studies that show these groups tend to be more involved in actively constructing their school careers. The level of interaction with classmates and school friends and the qualitative enrichment they might bring to LC students' HE projects is, however, highly contingent on contextual factors.

There are remarkable differences in the frequency and content of LC students' interactions, particularly with peers, depending on the tracks and schools in which they are enrolled. The interaction patterns and discussion topics of the students in the academic track, especially those in privileged schools, are similar to those of their classmates, but this only relates to a small group of students -(self-)selected on the basis of their results, ambition and, probably, parental involvement in their schooling -who incorporate dominant upper-class norms and practices [START_REF] Jack | The Privileged Poor. How Elite Colleges are Failing Disadvantaged Students[END_REF].

The configuration and role of MC students' personal networks with respect to their HE plans are less obvious. One of these students' distinctive features is that their search for information and advice is more limited to members of the nuclear family than in the other two groups, with friends seemingly providing only moral support. Mothers, in particular, seem to be their main reference, which is typical of the 'maternalistic' parenting style that [START_REF] Kellerhals | Les Stratégies Educatives des Familles[END_REF] found to be more present among LC families, but that might also be present among MC families having undergone a process of upward mobility. Also, the more heterogeneous contexts in which these students undergo family and school socialisation might explain the presence of interaction patterns that are sometimes closer to those of LC students and sometimes to those of UC students.

Conclusions

Our findings clearly show that students' interactions about future study plans with members of their personal networks are influenced by their social position, reflecting both dispositions acquired at home and family economic and cultural capital. While this is what our conceptual framework led us to expect, our research provides new leads concerning the specific role played by certain dispositions and capitals in terms of both network configuration and network content. Differences in network size, composition, and the weight given to information and advice provided by different persons reflect, first, different ways of relating to family members, acquaintances, and friends learned through primary socialisation and, second, students' cultural orientations and capacity to assess the cultural resources that these people can provide, which vary across social groups. Differences in network content, however, are clearly influenced by students' academic level and prior knowledge about the field of HE, as well as by their degree of concern about economic costs. Dispositions, especially aspirations, can also play a key role.

Our analysis of the impact of school contexts on the form and content of the personal networks on which students draw in making HE plans also sheds new insights on habitus persistence and change. Our results clearly show that students are unequally affected by their school environment, depending on their social class. The contrasting results between UC students, whose habitus remains very similar across contexts, and LC students, who change quite radically, at least when it comes to making HE plans, can be partly attributed, for the former, to their parents' strong control over their school careers [START_REF] Ball | Class Strategies and the Education Market. The Middle Classes and Social Advantage[END_REF][START_REF] Lareau | Unequal Childhoods[END_REF]) and, for the latter, to the fact that they constitute a minority selected and sponsored by their parents and teachers because of their good academic profiles [START_REF] Olivier | Channelling Students into Higher Education in French Secondary Schools and the Re-Production of Educational Inequalities. Discourses and Devices[END_REF]. These results, however, also show that the durability of primary dispositions depends on the strength with which they were enforced, which in turn rests on the homogeneity and complementary of the perspectives and actions of the main socialising agents. UC students have a highly internalised habitus regarding desirable HE futures and how to achieve them with the help of their parents and of selective groups of friends. This habitus has been nurtured at home and at school by parents and teachers who are convinced that this is their 'natural' path and who provide compatible role models and cultural skills. In contrast, most LC students are likely to have been raised in families where HE futures appear uncertain and where they receive contradictory explicit and implicit messages from parents, siblings, friends, and teachers. For significant changes to take place, it is necessary for these students to be immersed in school environments in which ambitious HE careers constitute a common norm among teachers, fellow students, and parents [START_REF] Roksa | Cultural Capital and Habitus in Context. The Importance of High School College-Going Culture[END_REF].

Our data has not allowed us to show that differences in the size and composition of students' personal networks, and in how they use them to obtain information and advice about HE plans and choices, contribute to reproducing class inequalities in access to HE. However, it is obvious that in HE systems such as the French one, which is both highly fragmented and hierarchical and in which HE admission procedures are frequently complex and opaque (van Zanten 2019), access to both 'cold' and 'hot' knowledge [START_REF] Ball | I Heard It on the Grapevine.' 'Hot' Knowledge and School Choice[END_REF] about the HE field is a key cultural asset. While LC students do frequently benefit from strong parental (and particularly maternal) emotional and moral support for their HE plans, they nevertheless remain crucially disadvantaged when it comes to these key cultural assets because they do not have parents with HE backgrounds and do not enjoy robust ties with teachers and career advisors [START_REF] Horvat | From Social Ties to Social Capital: Class Differences in the Relations between Schools and Parent Networks[END_REF][START_REF] Cox | It's Who You Know (and Who You Are): Social Capital in a School-Based Parental Network[END_REF]. This disadvantage can only be partly compensated by these students benefiting both from formal institutional support and from the informal influence and help of their classmates. Nevertheless, there is a strong argument here in favour of policies aiming to reduce inequalities in provision of educational services (notably in terms of the timing, amount and degree of personalisation of HE advice [START_REF] Mcdonough | Choosing Colleges: How Social Class and Schools Structure Opportunity[END_REF]Author et al. 2018;[START_REF] Gast | Reconceptualizing College Knowledge: Class, Race and Black Students in a College-Counseling Field[END_REF]) and segregation levels across the educational system.

Declaration of interest

All human subjects gave their informed consent prior to their participation in the research, and we protect the confidentiality of participants and institutions by excluding any identifying information. We also report no conflict of interest.

This study is part of a broader research project exploring how networks, institutions and markets influence the ways in which students from different social classes engage with HE (van Zanten

2019).

This platform, now called Parcoursup, underwent significant changes in 2018 after our study. A major difference is that students now no longer rank their choices[START_REF] Frouillou | Le Rôle des Instruments dans la Sélection des Bacheliers dans l'Enseignement Supérieur. La Nouvelle Gouvernance des Affectations par les Algorithmes[END_REF]).

At the most aggregated level, the INSEE Professions and socioprofessional categories nomenclature (whose initial designers both contributed to Bourdieu's training in statistics and were later influenced by his sociological

Because the vast majority of MC and UC students have two French parents (respectively,

78% and 92%), we can only explore differences according to immigrant background in the case of LC students. We compare students with two French parents, with one French parent and with two parents born abroad.

We also examined variations according to schools' administrative status (state/private) but these variations were less significant as our sample only allows us to compare UC students in the two 'privileged' state and private establishments and, for this reason but also for lack of space, we do not present them here.

Due to the smaller sample of MC students in professional tracks, we consider them together with those in technological tracks.

A reform of the academic lycée track in 2018 abolished these subtracks. Students in this track now follow a common core curriculum together with three optional subjects in Year 12 and two in Year 13[START_REF] Pin | The Impact on French Upper Secondary Schools of Reforms Aiming to Improve Students' Transition to Higher Education[END_REF].

Presently, French students are allocated to state lycées through an algorithm taking into account their choices and prioritising them according to place of residence, which remains the most important criterion, but also grades and scholarship status. Some prestigious state lycées such as the one in our sample managed until recently to use specific admission procedures, similarly to private lycées.

This term, which refers to the accumulation of advantages by high status individuals, was coined by the sociologists Robert K.[START_REF] Merton | The Matthew Effect in Science[END_REF] and was inspired by the Parable of the Talents in the biblical Gospel of Matthew.