This document presents a study analyzing the dynamics of interacting multiplex networks. The objectives are to analyze popular social networking platforms like Facebook and Twitter as multiplex networks through common users, and to study how interactions in one network layer can influence dynamics in another layer using a multiplex network model with different topologies. The study collects data from Facebook and Twitter to construct a multiplex network and identifies common users across the networks. It then analyzes citation and co-authorship networks as interacting layers to study how productivity and citations in one network correlate with the other network. Key results show influence of higher degree nodes on citations and collaboration patterns across the network layers.

1. Introduction
Objective I
Objective II
Conclusion
Analyzing Dynamics of Interacting Multiplex
Networks
Soumya Sarkar M.Tech. CSE 2nd Yr
Indian Institute of Technology Patna
Guided By : Dr. Joydeep Chandra
April 29, 2015
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

2. Introduction
Objective I
Objective II
Conclusion
Overview
Introduction
SNA
Motivation
Project Goals
Objective I
Data Collection
Structuring
Analysis
Objective II
Preprocessing
Preliminary analysis
Final Analysis
Conclusion
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

3. Introduction
Objective I
Objective II
Conclusion
SNA
Motivation
Project Goals
Representing Entities and Relations
Representing physical systems as networks yeilds many interesting insights
Studying properties of the network helps us understand the system processes
Understanding system processes has applications in building recomender
systems,in targeted advertisement,viral marketing even in drug design.
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

4. Introduction
Objective I
Objective II
Conclusion
SNA
Motivation
Project Goals
Drawbacks of Traditional Methods
Traditional graph theory deals with node centric properties
It is inadequate to give us an idea about system wide properties
It is not sufficient to deal with graphs that represent real world networks
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

5. Introduction
Objective I
Objective II
Conclusion
SNA
Motivation
Project Goals
Example
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

6. Introduction
Objective I
Objective II
Conclusion
SNA
Motivation
Project Goals
Current Research
In the Last decade large number of real life networks have been studied as
Complex Networks
Static properties such as Degree Distribution,Clustering Coefficient,Small World
Property, Assortativity etc has been studied widely.
Dynamic properties such as Preferential Attachment,Percolation,Ressilience has
also been topics of interest.
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

7. Introduction
Objective I
Objective II
Conclusion
SNA
Motivation
Project Goals
Multiplex Networks
1. Networks donot exist in isolation
2. Multiple networks function as single ecosystem
3. As an evidence when a video goes viral it happens due to collaboartion of
multiple social network platforms.
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

8. Introduction
Objective I
Objective II
Conclusion
SNA
Motivation
Project Goals
Why Multiplex
Research in multiplex
network is still in its
infancy
Many real life networks
have not been seen from
the point of view of
multiplex network.
Visualizing networks as
multiplex network can
help us analyze effect of
growth of one layer on
another.
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

9. Introduction
Objective I
Objective II
Conclusion
SNA
Motivation
Project Goals
Project objectives
1. Study Popular Social Networking Platforms like Facebook,Twitter and establish
that they behave as multiplex network via common agents.
2. Given a Mulitplex network with different topology establish that the interaction
of one layer can influence dynamics in another layer.
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

10. Introduction
Objective I
Objective II
Conclusion
Data Collection
Structuring
Analysis
Seed Data Collection
To look at social networking platforms from the point of view of multiplex
network we required specific real world data.
Seed data must have valid profiles at both target platforms
The initial challenge was collecting such a dataset using automated techniques.
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

11. Introduction
Objective I
Objective II
Conclusion
Data Collection
Structuring
Analysis
We searched platforms which had
self indentification feature like
Blogger.com,Goolge+ .
After collecting seed data I
validated them using automated
techniques.
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

12. Introduction
Objective I
Objective II
Conclusion
Data Collection
Structuring
Analysis
Neighbourhood Exploration
In Facebook due to the unavilability of any API browser automation tool
selenium was used
Selenium is used in junction with a headless webkit PhantomJS which simulates
a user session in Facebook.
In case of twitter specific API’s i.e Restfull API version 1.1 are available to
perform our desired task.However this API comes with rate limiting constraint
hence it is necessary to stall the data collection process to synchronise it with
rate liming constraint when required.
Data obtained is simultaneously structured into a Directed Graph using
python-igraph library and stored in disk in xml format
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

13. Introduction
Objective I
Objective II
Conclusion
Data Collection
Structuring
Analysis
Data Visualization
Figure : (a) Facebook Figure : (b) Twitter
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

14. Introduction
Objective I
Objective II
Conclusion
Data Collection
Structuring
Analysis
Matching
1. We required profile attributes to identify common entities in the neighborhood
of a user.
2. We used user name as profile attribute because it is publicly available
3. We found active nodes in the neighborhood of the seed node who were present
in both layers
4. It is established by the data collected that this different platform have logical
connections through common nodes.
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

15. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
1. According to our second objective we wanted to perform microscopic analysis of
a multiplex network in terms of its constituent layers
2. We want to look at a network with multiplex properties , enormous size and
growing at a rapid rate.
3. Both coauthorship and citation network have been analysed individually but this
is the first time they are analysed together with author as dynamic entities in
either layers
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

16. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
ArnetMiner Data Format
#*Automated Deduction for Many-Valued Logics.
#@Matthias Baaz,Christian G. Fermller,Gernot Salzer
#t2001
#cHandbook of Automated Reasoning
#index628
#%71399
#%71859
#%71848
#!
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

17. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
Table
General Information about DataSet
Total No Of Papers 2146330
Total No Of Unique Authors 1232541
Average No of Authors per paper 2.726
Average No of Papers per Author 4.74782
Year 1930-2013
Table : 1
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

18. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
220000
1990 1995 2000 2005 2010
NoofUniqueAuthors
years
Unique Author
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
1990 1995 2000 2005 2010
PaperCount
Year
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

19. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
Building Temporal Graph
1. Essential information like paper id, author name, year, citation information were
extracted from the data
2. Indexes were formed based on paper ids, author names, citing for fast retrieval.
3. Three types of Graphs were constructed from the data recording scientific
productivity and citation obtained from 1989 to 2010.
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

20. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
1e-06
1e-05
0.0001
0.001
0.01
0.1
1
1 10 100 1000 10000
Probabilityk
Degree k
Citation Network
Coauthorship Network
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

21. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
Nature of this plot show Power Law Distribution where
P(k) ∼ k−α
Our intuition is patterns of interaction which led to this nature is not
independent
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

22. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
0
20
40
60
80
100
1990 1995 2000 2005 2010
AvgRate
Year
top 3000
top 100
Nature of this plot shows the average
rate of collaboration of top 3000
highly cited authors and top 100 over
the span of their career for 20 years
We see nodes with higher productivity
in one layer performs significantly
better in the corressponding layer too
although eventually average rate of
productivity becomes steady
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

23. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
0
0.2
0.4
0.6
0.8
1
1.2
1-40 41-80 81-120 121-160 161-200 201-240
Fraction
Degree Range
Regular
Reciprocated
It has been shown by various
researchers that scientific network is
disassortative with respect to degree
Using both networks we investigated
how mixing with respect to degree
corresponds with citation network.
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

24. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
2
4
6
8
10
12
14
16
18
1-10
11-20
21-30
31-40
41-50
51-60
61-70
71-80
81-90
91-100
101-110
111-120
121-130
AverageCitations
Degree Range
avg citations Here average citations between
researchers of similar degree is shown
Collaborators of higher degree refer
each others work significantly
compared to collaborators of lower
degree
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

25. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
We have divided the citation received by top cited papers into 3 categories
Self citation, Co-author citation and Distant Citation
In the next couple of graphs we have shown how these different citations coexist
at each time instance and how top cited papers of a particular time period
recieve these citations over a span of 10 years.
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

26. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
0
20
40
60
80
100
1990 1995 2000 2005 2010
Percentage
Year
Self-Citations
Coauthor Citations
Distant Citations
0
20
40
60
80
100
1990 1995 2000 2005 2010
Percentage
Year
Self-Citations
Coauthor Citations
Distant Citations
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

27. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
Citation Effect
To quantify influence of citation on collaboration we have extracted top cited
papers in two different time instances and identified authors who have cited
these titles.
We have calculated fraction of the citing authors within the 1st and 2nd hop of
the cited authors.
We have monitored the neighborhood of the cited authors for next 10 years and
calculated the fraction of citing authors for every 2yrs
We notice a positive increase in the fraction of citing authors in the
neighbourhood of cited authors.
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

28. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
5
10
15
20
25
30
35
1990 1992 1994 1996 1998 2000 2002
Percentage
Year
First Hop
Second Hop
5
10
15
20
25
30
35
40
45
50
1998 2000 2002 2004 2006 2008 2010
Percentage
Year
First Hop
Second Hop
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

29. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
Figure : t1 Figure : t2
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

30. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8
FrequencyofCiteBack
Year
citeback fraction
1. In terms of author author citation
reciprocation of citation is an
interaction of considerable
interest to us.
2. Among all the reciprocation that
we have encountered, in this
graph I have plotted the fraction
of reciprocation received with
respect to time
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

31. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

32. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
0
20000
40000
60000
80000
100000
120000
1989-2007
1991-2007
1993-2007
1995-2007
1997-2007
1999-2007
2001-2007
2003-2007
2005-2007
TotalCitebacksandCollaboratedCitebacks
Time Span
Cite Backs
Collaborated Cite Backs
1. In this graph I have shown the
volume of citebacks recieved in
each time epoch and the
calculated cite backs received due
to collaboration and vice versa
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

33. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
Community Distribution
1. One of the most interesting findings of random graph theory is the existence of
a critical probability at which a cluster forms.
2. It indicates the existence of a critical probability pc such that below pc the
network is composed of isolated clusters but above pc a giant cluster spans the
entire network.
3. Using Fast Folding Community Finding Algorithm I have shown the community
distribution of either layers in the following graphs
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

34. Introduction
Objective I
Objective II
Conclusion
Preprocessing
Preliminary analysis
Final Analysis
0 10000 25000
0.000.100.20
Citation Network
Cluster Size k
p(k)
0 10000 20000 30000
0.00.20.4
Coauthor Network
Cluster Size k
p(k)
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

35. Introduction
Objective I
Objective II
Conclusion
Conclusion and Future Work
Results of our emperically analysis show that ensemble of networks can be
visualized as multiplex netowrk
Given an interaction in one layer can induce link generation in another layer
Based on this observation we plan to investigate further in the possibility of
generating giant component in one layer through interaction in another layer.
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

36. Introduction
Objective I
Objective II
Conclusion
References
1. Predicting scientific success based on coauthorship networks Emre Sarigl, Ren Pfitzner * , Ingo Scholtes, Antonios Garas and
Frank Schweitzer
2. Jie Tang, Jing Zhang, Limin Yao, Juanzi Li, Li Zhang, and Zhong Su. ArnetMiner: Extraction and Mining of Academic Social
Networks. In Proceedings of the Fourteenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
(SIGKDD’2008). pp.990-998
3. A.-L. Barab asi et al., Scale-free networks: a decade and beyond, science, vol. 325, no. 5939, p. 412, 2009.
4. M. E. Newman, The structure and function of complex networks, SIAM review, vol. 45, no. 2, pp. 167256, 2003.
5. J. Ugander, B. Karrer, L. Backstrom, and C. Marlow, The anatomy of the facebook social graph, arXiv preprint
arXiv:1111.4503, 2011.
6. The simultaneous evolution of author and paper networks Katy Borner, Jeegar T. Maru, and Robert L. Goldstone
7. J. Leskovec and A. Krevl, SNAP Datasets: Stanford large network dataset collection. http://snap.stanford.edu/data, June 2014.
8. M. Kivel a, A. Arenas, M. Barthelemy, J. P. Gleeson, Y. Moreno, and M. A. Porter, Multilayer networks, arXiv preprint
arXiv:1309.7233, 2013.
9. The structure of scientific collaboration networks M. E. J. Newman
10. Coauthorship and citation patterns in the Physical Review Travis Martin,* Brian Ball,Brian Karrer,and M. E. J. Newman WEB),
2010 12th International Asia-Pacific, pp. 236242, IEEE, 2010.
11. A. A. Hagberg, D. A. Schult, and P. J. Swart, Exploring network structure, dynamics, and function using NetworkX, in
Proceedings of the 7th Python in Science Conference (SciPy2008), (Pasadena, CA USA), pp. 1115, Aug. 2008.
12. M. Bastian, S. Heymann, and M. Jacomy, Gephi: An open source software for ex- ploring and manipulating networks, 2009.
13. Modes of Collaboration in Modern Science Beyond Power Laws and Preferential Attachment Stasa Milojevic
14. Persistence and uncertainty in the academic career Alexander M. Petersen a,1 , Massimo Riccaboni b,c,d , H. Eugene Stanley
e,1 , and Fabio Pammolli
15. Reputation and Impact in Academic Careers Alexander M. Petersen, Santo Fortunato,Raj K. Pan,Kimmo Kaski,Orion
Penner,Armando Rungi,Massimo Riccaboni,H. Eugene Stanley,and Fabio Pammolli
16. Citation interactions among computer science fields: a quantitative route to the rise and fall of scientific research Tanmoy
Chakraborty,Sandipan Sikdar,Niloy Ganguly,Animesh Mukherjee
Soumya Sarkar M.Tech. CSE 2nd Yr MTP

37. Introduction
Objective I
Objective II
Conclusion
Thank You
Soumya Sarkar M.Tech. CSE 2nd Yr MTP