Sofia Dokuka, Diliara Valeeva, Maria Yudkevich (HSE) Formation and evolution mechanisms in online network of students: the Vkontakte case AIST Conference 2015, http://aistconf.org

1. Formation and evolution mechanisms in online network
of 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

2. Backgroung
Computer Science stream: Analysis of node-level characteristics and
their 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 very
beginning (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

3. Network growth models
Erdos-Renyi model is obtained by starting with a set of n isolated
nodes and adding successive edges between them at random. The
model does not adequately describe properties of real networks.
Barabasi-Albert model begins with an initial connected network and
then new nodes are added to it. The probability of connecting to the
particular node is proportional to the number of edges that the
existing nodes already have. The model captures well the degree
distribution, but cannot describe high clustering.
Watts-Strogatz model begins from a regular ring lattice with n
nodes which is connected to k neighbors. The number of closed
triads in the network will be relatively high. To provide the short
APL, the option of edge rewiring is added. The edge disconnects
from 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

4. This study
Research question: How does the social network form and evolve?
Network has a restricted and known number of participants (one
cohort 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

5. Case description
We investigated the formation and evolution of student online social
network 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 accepted
at full-tuition places;
Overall, in 2014, 97 students who studied both at tuition-free and full
tuition places were matriculated;
In this university, students study in groups of up to 30 students. The
division into study groups is random;
Lectures are usually delivered to several groups simultaneously, while
seminar classes are delivered to each group separately;
A very small number of students in our sample knew each other
before the university.
S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 5 / 19

6. Data collection procedure
We found students Vkontakte profiles according to their names in a
public list of enrolled students. Overall - 97 students, we collected
networks of 71 students;
We gathered publicly open data about student ego-networks using
Vkminer;
13 waves with an average time period between waves in one week and
fixing for important events.
S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 6 / 19

7. 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

8. Vkontakte networks
Figure: The network growth. Nodes are students Vkontakte accounts, edges are
friendship links between accounts. The size of the node reflects the degree
centrality. Nodes are fixed at the same place
S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 8 / 19

9. Method
Conditional Uniform Graph test (CUG-test)(Anderson et al, 1999)
compares network graph-level indices with the same measures of the
random networks;
We compare the observed network at each timepoint with three
random 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 a
mean 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

10. 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

11. Results (2): Network APL and diameter
Figure: Average path length dynamics.
Vertical line corresponds to September
1, start of the academic year.
Figure: Network diameter 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 11 / 19

12. Results (3): Network assortativity and giant component
Figure: Network assortativity dynamics.
Vertical line corresponds to September
1, start of the academic year.
Figure: Giant compotent size 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 12 / 19

13. 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 the
observed network well-described by random networks. At the
beginning, these indices are small because there are few edges in the
network. After the September 1 both measures increased. As
students create many links, indices decrease.
The degree assortativity for the observed network during the first
observations was much higher (0.01%) than can be expected by
random. After the students offline acquaintance, assortativity
decreased.
The size of the giant component evolves in a similar way for both
observed and simulated networks. The number of nodes in the
random networks tends to be higher than in an observed one (sig at
0.01%).
S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 13 / 19

14. Summary
We trace a tendency of friends of friends to be connected in real
world social networks;
The average path length, network diameter and giant
component dynamics shows that at the beginning students tend to
join giant component and arrange connections with their peers. At
the late moments of observation students form dense groups;
Degree assortativity dynamics shows the absence of degree-based
hierarchy after September 1. Students befriend each other without
preselection. The potential aim of this process is to add the
maximum amount of classmates to gather information from the new
environment.
S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 14 / 19

15. Formation and evolution mechanisms in online network of
students
Figure: Connected component
attachment mechanism
Figure: Brokerage mechanism
The connected component mechanism implies that nodes look for an
option to join the connected component. Connectedness with peers
might be useful for receiving new information (Vaquero, 2013);
The brokerage mechanism based on the intuition that two people with
a 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

16. Thank you for attention!
Questions?
S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 16 / 19

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

18. University admission procedure
In Russia students might enroll in universities by several different
trajectories.
1 Olympiads. Olympiads are all-Russian competitions for talented
school students in a wide range of subjects. Students that become
winners and awardees of these Olympiads can be accepted to any
university of their choice without additional exams free of tuition;
2 USE. The USE is a standardized test in various subject areas and has
a unified grading scale throughout all of Russia. Universities accept
students 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

19. Vkontakte
Vkontakte is a popular Russian social networking site with monthly
audience 55 million users. Vkontakte interface and options are very similar
to 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 data
directly from the site;
3 VKminer software (http://linis.hse.ru/en/soft-linis) allows to
download publicly available data from the Vkontakte site. Developed
by Laboratory for Internet Studies.
S. Dokuka, D. Valeeva, M. Yudkevich (HSE) AIST 2015, Yekaterinburg April 10, 2015 19 / 19