Formation and evolution mechanisms in online networkof students: the Vkontakte case

Sofia Dokuka, Diliara Valeeva, Maria Yudkevich

Center for Institutional Studies, NRU HSE, Moscow, Russia

sdokuka@hse.ru

April 10, 2015

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 1 / 19

Backgroung

Computer Science stream: Analysis of node-level characteristics andtheir changes (Backstrom 2006, Leskovec 2008, Kairam 2012)

Sociological stream: Coevolution of social network and actors’behavior (Snijders 2010, Lewis 2012)

No studies about the evolution of the social network from the verybeginning (no ties between actors) to the end of the network growth.

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 2 / 19

Network growth models

Erdos-Renyi model is obtained by starting with a set of n isolatednodes and adding successive edges between them at random. Themodel does not adequately describe properties of real networks.

Barabasi-Albert model begins with an initial connected network andthen new nodes are added to it. The probability of connecting to theparticular node is proportional to the number of edges that theexisting nodes already have. The model captures well the degreedistribution, but cannot describe high clustering.

Watts-Strogatz model begins from a regular ring lattice with nnodes which is connected to k neighbors. The number of closedtriads in the network will be relatively high. To provide the shortAPL, the option of edge rewiring is added. The edge disconnectsfrom one of its nodes and randomly connects to another node.

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 3 / 19

This study

Research question: How does the social network form and evolve?

Network has a restricted and known number of participants (onecohort of students);

Online network from the very formation till stabilization.

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 4 / 19

Case description

We investigated the formation and evolution of student online socialnetwork in one of the top Russian universities.

Students get accepted to university in 3 groups of applicants:according to Olympiad results, USE results, and others get acceptedat full-tuition places;

Overall, in 2014, 97 students who studied both at tuition-free and fulltuition places were matriculated;

In this university, students study in groups of up to 30 students. Thedivision into study groups is random;

Lectures are usually delivered to several groups simultaneously, whileseminar classes are delivered to each group separately;

A very small number of students in our sample knew each otherbefore the university.

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 5 / 19

Data collection procedure

We found students Vkontakte profiles according to their names in apublic list of enrolled students. Overall - 97 students, we collectednetworks of 71 students;

We gathered publicly open data about student ego-networks usingVkminer;

13 waves with an average time period between waves in one week andfixing for important events.

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Descriptive statistics

Figure: Number of nodes dynamics Figure: Number of edges dynamics

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 7 / 19

Vkontakte networks

Figure: The network growth. Nodes are students Vkontakte accounts, edges arefriendship links between accounts. The size of the node reflects the degreecentrality. Nodes are fixed at the same place

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 8 / 19

Method

Conditional Uniform Graph test (CUG-test)(Anderson et al, 1999)compares network graph-level indices with the same measures of therandom networks;

We compare the observed network at each timepoint with threerandom networks of the same size (based on Erdos-Renyi,Barabasi-Albert, and Watts-Strogatz models);

The graph-level indices of the random networks were calculated as amean value from the distribution of 10000 random networks;

Indices for comparison: clustering coefficient, size of giant component,average path length, network diameter, and degree assortativity.

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 9 / 19

Results (1): Clustering coefficient

Figure: Clustering coefficient dynamics. Vertical line corresponds to September 1,start of the academic year.

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 10 / 19

Results (2): Network APL and diameter

Figure: Average path length dynamics.Vertical line corresponds to September1, start of the academic year.

Figure: Network diameter dynamics.Vertical line corresponds to September1, start of the academic year.

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 11 / 19

Results (3): Network assortativity and giant component

Figure: Network assortativity dynamics.Vertical line corresponds to September1, start of the academic year.

Figure: Giant compotent size dynamics.Vertical line corresponds to September1, start of the academic year.

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 12 / 19

Results: description

The clustering coefficient of the observed network was much higher(sig at 0.01%) than for any random network.

The dynamics of average path length and diameter for theobserved network well-described by random networks. At thebeginning, these indices are small because there are few edges in thenetwork. After the September 1 both measures increased. Asstudents create many links, indices decrease.

The degree assortativity for the observed network during the firstobservations was much higher (0.01%) than can be expected byrandom. After the students offline acquaintance, assortativitydecreased.

The size of the giant component evolves in a similar way for bothobserved and simulated networks. The number of nodes in therandom networks tends to be higher than in an observed one (sig at0.01%).

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 13 / 19

Summary

We trace a tendency of friends of friends to be connected in realworld social networks;

The average path length, network diameter and giantcomponent dynamics shows that at the beginning students tend tojoin giant component and arrange connections with their peers. Atthe late moments of observation students form dense groups;

Degree assortativity dynamics shows the absence of degree-basedhierarchy after September 1. Students befriend each other withoutpreselection. The potential aim of this process is to add themaximum amount of classmates to gather information from the newenvironment.

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 14 / 19

Formation and evolution mechanisms in online network ofstudents

Figure: Connected componentattachment mechanism

Figure: Brokerage mechanism

The connected component mechanism implies that nodes look for anoption to join the connected component. Connectedness with peersmight be useful for receiving new information (Vaquero, 2013);

The brokerage mechanism based on the intuition that two people witha common friend tend to become friends with each othe (Burt, 2004).

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 15 / 19

Thank you for attention!Questions?

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 16 / 19

Additional materials

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 17 / 19

University admission procedure

In Russia students might enroll in universities by several differenttrajectories.

1 Olympiads. Olympiads are all-Russian competitions for talentedschool students in a wide range of subjects. Students that becomewinners and awardees of these Olympiads can be accepted to anyuniversity of their choice without additional exams free of tuition;

2 USE. The USE is a standardized test in various subject areas and hasa unified grading scale throughout all of Russia. Universities acceptstudents with the highest USE scores free of tuition;

3 Students that are not Olympiad winners and have low USE scores,might study with full tuition.

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 18 / 19

Vkontakte

Vkontakte is a popular Russian social networking site with monthlyaudience 55 million users. Vkontakte interface and options are very similarto Facebook, it is often called ”Russian Facebook”.

1 Vkontakte is very popular among youth and students;

2 Vkontakte has an open API system which allows to download datadirectly from the site;

3 VKminer software (http://linis.hse.ru/en/soft-linis) allows todownload publicly available data from the Vkontakte site. Developedby Laboratory for Internet Studies.

S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 19 / 19