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Table of contents
Peer-group membership is also a part of identity as the group of friends to which adolescents belong helps define who they are [ 39 ]. We might expect, for example, that high performing students seek friendship with other high performing students as part of their academic identity formation. There is evidence that the importance of pears peaks in the early adolescence and then gradually declines when young people develop a mature sense of autonomy [ 31 ].
Homophily in academic performance has been studied with network data collected with questionnaire-based surveys [ 4 , 5 ]. The design of these studies makes it hard to follow the temporal evolution of social networks. The availability of new technologies and big datasets provides researchers with novel tools to observe the dynamics of social networks with high temporal precision. For example, the temporal structure of social networks has been reconstructed by email data [ 40 ], computer game logs [ 41 ], or interactions on learning management system platforms [ 42 ].
The quantification of social ties remains a challenging task [ 43 ]. Even traditional approaches that are based on self-reported friendship ties may contradict the common definition of friendship. For example, it was shown that only half of self-reported friendship links was reciprocal despite the fact that almost all of them were perceived as reciprocal [ 44 ]. Alternatively, friendship links may be inferred from digital records of human behaviour, allowing to track the detailed evolution of social ties [ 45 ], including those among high school students [ 46 ].
In this paper, we use a unique anonymized dataset to observe the temporal formation of academic homophily based on social interactions between Russian students from a public high school and a university. VK users create their profiles with information about their identity, education, interests, etc.
The use of the real name is required by VK. Users may indicate other users as their friends. VK friendship is mutual and requires confirmation. However, using VK friendship links is not the most efficient way to study the dynamical evolution of actual friendships, since only information about the current friendship is available, which makes it practically impossible to extract the dynamics of VK friendship links.
It is also impossible to distinguish active friendship ties from obsolete ones since VK friendship links are rarely dissolved.
Social network analysis - Wikipedia
This approximation of actual friendships by social interaction strengths allows us to track the effective network evolution between students with much higher precision see S1 Fig. The network of university students seniors on March is shown in Fig 2. Previous studies on the Facebook or its Russian analog VK have focused on the relatively static friendship marking options that are provided by the sites [ 50 — 52 ]. This dataset not only allows us to quantify the extent of academic homophily among students but also to see its detailed evolution over time. In particular, we are able to clarify the mechanism behind the emergence of academic homophily from an initially homogeneous population across several years.
Color represent the performance GPA of students across the whole period of studies. There is visible clustering of students with similar GPA. We use two datasets of academic performance records measured as grade point averages GPA , one with students from the 5th to 11th grades age from 11 to 18 of a Russian public high school in Moscow for reasons of anonymity we do not state the name of the school , the other with 5, bachelor students of the Higher School of Economics in Moscow. High school students receive their grades at the end of each trimester, their GPAs for the last 5 trimesters were available.
It contains information about their GPAs for the current semester along with the aggregated average GPA across the whole period of their studies. Note that grades are different for high school and university. For high school grades range from 2 worst to 5 best , for university from 4 worst to 10 best. The average GPA of a student across the entire available time period we denote by.
The average GPA for high school students and the cohorts of university students are presented in S1 Table. To generate a proxy for the temporal friendship interaction network between students we use the popular SNS VK, whose main component is a user-generated news feed. This feed contains all content that was generated posted by users and is generally visible to friends only.
In particular, it is possible to download user profiles from particular educational institutions and within selected age ranges. For each user, it is possible to obtain the list of their friends and the content that was published by them along with the VK identifiers of users that liked this content.
Posting times are known with a time resolution of one second. The matching procedure was performed by authorized representatives of the high school and the Higher School of Economics, respectively. After the matching procedure, all names and VK identifiers were irrevocably deleted. For detailed information about time periods corresponding to collected network data see S6 Fig. The resulting datasets were transferred to the Institute of Education, which made it available for research in fully anonymized form.
We first demonstrate the existence of academic homophily and then try to understand its origin. For all groups of students we find strong homophily. I X t can not only be computed for friends social distance 1 but also for friends of friends social distance 2 , and friends of friends of friends social distance 3 , etc. In Fig 3 we fix X to be the 50th above average students a and b and 80th excellent students percentile c and d , respectively. Significance was tested with a permutation test 10, permutations , see Methods.
Note that the corresponding values at the first time point are smaller, , , ,. Observed increase in probability I X that a student is in the top X th percentile of students, given that their friends are also in the top X th percentile. Results for the high school are shown in a and c , for university in b and d.
The social distance of 1 means friends, the social distance of 2 means friends of friends and the social distance of 3 means friends of friends of friends. This result holds independent from the method used. In Fig 4 we show the time evolution of homophily over 1. We employ a transparent definition of a Homophily Index , H see Methods. Homophily increases with time by almost a factor of 2 circles. The significance of the observed effect is measured with a randomization test triangles , where grades were reshuffled randomly between the nodes in the network.
It is amazing that when the GPAs of individual students are fixed to their temporal average crosses , practically the same increase of homophily is observed, which signals the dominance of network restructuring. Results can be understood with a simple model squares. Vertical bars are standard deviations. Due to the second argument above the explanation of the observed homophily increase can only come through changes in social networks over time, i. A simple model allows us to understand the situation. It assumes that whenever students select new friends they prefer students who are more similar to them than their current friends.
Every student i is endowed with a fixed GPA constant. There exists an initial friendship network that we initialize with the observed network at timestep 1,. The results of the model are presented in Fig 4 boxes. The experimental homophily increase is recovered. Remarkably, for all student groups, the model is able to reproduce even details in the empirical GPA distances between stable, discontinued, and new friendships, see S3 Table.
We have to show that the homophily increase is not explained as a trivial consequence of network densification. In both datasets we observe that friendship networks are dynamically changing over time. In Fig 5 the relative change of the average degree and the clustering coefficient of the networks are shown in comparison with the relative change of homophily. To see that the observed homophily increase is not a trivial consequence of network densification, observe that while for the high school degree and clustering increase, for university seniors they decrease. In both cases homophily increases.
This is a first indication that degree and clustering are not the drivers of homophily change. As a second indication we test if H and I X are significant with respect to a permutation test that preserves network topology. This is indeed the case see Methods. Thirdly, by re-defining time intervals in a way that for each time interval the average degree is approximately the same, we find the same homophily increase see S3 Fig , indicating that the degree is not an explanatory variable.
While the network of seniors becomes sparser, there is a densification of the high school network inset. Therefore degree and clustering coefficients can not be the drivers behind the observed homophily increase in both groups. Finally, in S4 Fig we show that there exist slight gender differences in the homophily increase. While both genders show about the same increase over time, the homophily index H is slightly larger for females in the sophomore and senior groups, and larger for males for the high school students and juniors.
However, the noise in our data is too large to confirm that homophily indeed peaks in early adolescence, as seen in [ 57 ]. We studied a unique dataset containing the academic performance of high school and university students together with detailed information about the evolution of their social ties.
In accordance with previous research [ 2 , 4 , 5 , 50 ] we found strong homophily in academic performance. The strength of academic homophily is found to be stronger than for homophily in sexual activity [ 58 ] or alcohol abuse among adolescents [ 59 ] but weaker than for homophily in smoking marijuana [ 59 ], or for age [ 54 ]. We are not only able to demonstrate the strong homophily in academic performance but also to monitor how it emerges from a homogenous population and how it solidifies over time.
We show that the observed gradual homophily increase can be explained predominantly by the process of social selection, meaning that students re-arrange their local social networks to form ties and clusters of individuals that have similar performance levels. We could exclude the alternative explanations of social adaptation and co-evolution of social ties and performance.
With a series of tests we ruled out the possibility that the increase of homophily results from adapting their academic performance to the one by their close friends. As an important consequence, this means that there are no indications for a pull effect, where groups of friends with good grades stimulate poor performing friends to increase their performance. The opposite effect of a negative group influence on students is also not found. It can be concluded that academic homophily in the studied groups arises and strengthens almost entirely through network re-linking. We are able to understand the social-selection based homophily increase with a simple dynamical one-parameter model.
Social Integration and Support
Note that even though this model is much simpler than others previously used [ 60 ], remarkably it is able to recover the increase over the whole time period for all groups, and even allows to understand details of the dynamics. It would be interesting to see in further work if these findings hold more generally also true for other student groups with different social contexts and in different countries.
It is important to note that the observed changes in social ties might be driven or facilitated by various factors. In the absence of ability tracking, other institutional factors may play a role in the segregation by academic achievements. For example extracurricular activities may provide an additional opportunity for similar individuals to meet and to from friendship ties [ 61 ]. Future research is needed to clarify the role of such specific factors.
Our findings might shed light or even confirm that access does not necessarily lead to equity. We find indications that physical mixing of students in the same educational institution does not lead to a homogeneous mixing of social ties. Even if the initial distribution is rather homogenous, students constantly re-organize their social network during the studies, which eventually results in segregation by academic performance. It is possible to conjecture that this mechanism is potentially reinforced by the accessibility of modern information technologies where maintaining links does not require physical presence anymore.
Academic achievements are the result of various factors, ranging from innate abilities to teacher qualification and family background. For example, Russian universities select students solely on the basis of their final school examination. Thus, academic achievements determine which students are selected for elite universities and which are not.
As social networks play a crucial role in social mobility [ 62 , 63 ], a selective university may provide a unique opportunity to create ties that will benefit students in the future. However, if initially low-performing students from a disadvantaged background predominantly create ties with other lower-performing students it significantly reduces their upward social mobility and may explain the persistence of inequality in societies. One of the challenges in understanding correlations of traits between connected individuals is to test if the observed homophily effect is significant or if it results trivially from the topology of the underlying network.
To test for this we employ a typical permutation test, see e. We repeat this procedure 10, times to obtain a distribution of the measures H and I X. We can then test the null hypothesis that GPAs are independent of network topology, and to compute corresponding p -values. The maximum observed value is or 0. The steep increase in September marks the beginning of studies.
Some students knew each other before the matriculation. Females have better grades on average. GPAs and their variance do practically not change with time. It is therefore possible to re-define new time intervals in such a way that for each time interval the average degree in the network is approximately the same. Clearly the homophily index H increases as before, indicating that the degree is not an explanatory variable. The same argument holds for the clustering coefficient. While both genders show about the same increase over time, it is larger for females in the sophomore and senior groups, and larger for males for the high school students and juniors.
Since there are only 4 possible values of grades scores possible for the individual subjects, we expect to observe less stable results than for the GPA. However, the general pattern of homophily increase over time holds, for mathematics it is not much pronounced. This period is equal to 3. The temporal GPA data, , was also collected for the last 3 semesters for all 3 cohorts arrows.
As students do not study in summer, we assume the same performance at that period as at the last available time point i. Mean values and standard deviations in brackets are presented. Females have better grades than males on average. The influence of gender is also significant, males have lower grades also after controlling for their previous GPA. The average GPA of friends at the previous time point is not significant. Comparable results are obtained with the model. We thank Dr. Browse Subject Areas? Click through the PLOS taxonomy to find articles in your field.
Abstract Homophily, the tendency of individuals to associate with others who share similar traits, has been identified as a major driving force in the formation and evolution of social ties. Funding: The authors received no specific funding for this work. Introduction Homophily is the tendency of humans to associate with others who share similar traits.
Download: PPT. Fig 1. Two basic mechanisms to understand the origin of homophily. Fig 2. Snapshot of the friendship network of university students. Results We first demonstrate the existence of academic homophily and then try to understand its origin. Fig 3. Homophily of students with good a and b , and excellent grades c and d , as a function of social distance. Fig 4. Evolution of homophily Homophily index in friendship networks of high school a and university students b. It was shown that school-entry academic skills have large predictive power for later academic performance [ 55 ], and that academic performance might be heritable [ 56 ].
We find the persistence of performance in our data. The average GPA over high school students 3. Similar results are observed for the university students, with an average GPA of 7. The results are presented in S2 Table. Again, this suggests that GPAs are rather stable over time and are almost fully determined by the GPA at the previous time point.
The regression shows no evidence for an adaptation effect. Social selection and network re-organization Due to the second argument above the explanation of the observed homophily increase can only come through changes in social networks over time, i. Fig 5. The network properties degree and clustering change over time relative changes are shown, first time point is 1. Discussion We studied a unique dataset containing the academic performance of high school and university students together with detailed information about the evolution of their social ties.
Randomization test One of the challenges in understanding correlations of traits between connected individuals is to test if the observed homophily effect is significant or if it results trivially from the topology of the underlying network. Supporting information.
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S1 Text. S1 Fig. S2 Fig. Average GPA for high school and university students inset over time. S3 Fig. In the high school data the network is getting more connected over time. S4 Fig. There are no consistent differences in gender. S5 Fig. Homophily increase varies from subject to subject. S6 Fig. Time schedule of data collection for university a and high school b students.
S1 Table. S2 Table. Coefficients from the regression model. Areas of Interest:. Phone number:. Fax number:. His lab uses both observational and experimental methods to study these phenomena, exploiting techniques from sociology, computer science, biosocial science, demography, statistics, behavior genetics, evolutionary biology, epidemiology, and other fields. To the extent that diverse phenomena can spread within networks in intelligible ways, there are important policy implications since such spread can be exploited to improve the health or other desirable properties of groups such as cooperation or innovation.
Finally, some work in the lab examines the biological determinants and consequences of social interactions and related phenomena, with a particular emphasis on the genetic origins and evolutionary implications of social networks. The author of several books and over articles, Christakis was elected to the Institute of Medicine of the National Academy of Sciences in and was made a Fellow of the American Association for the Advancement of Science in Publications Books N.
Christakis and J. Nishi, H. Shirado and N. Chabris, B. Hebert, D. Benjamin, J. Beauchamp, D. Cesarini, M. Johannesson, P. Magnusson, P. Atwood, J. Freese, T. Hauser, R. Christakis, D. Landon, N.