Inspecting dynamics of networks opens up a new dimension in the understanding or mechanisms behind real-world systems. Involving the time factor may help identifying previously hidden (or otherwise hard to recognize) phenomenon and/or patterns compared to static analysis, like individuals periodically changing between groups within a community.
Concentrating on edge dynamics, we defined a set of dynamic network models with various rules (including creating new and relinking edges randomly, by using assortative mixing or preferential attachment strategies) to analyize the evolution of different network properties. Starting from an initial network created by classical network models (like the Erdos-Renyi model) we examined the evolution of basic structural network properties (including density, clustering, average path length, number of components, degree distribution and betweennes centralities). The structure of the snapshot network (i.e., the network that is actually observed in a given instant of time) and the cumulative network (i.e., the network that is constructed by collecting and aggregating several samples of snapshot networks over a period of time) is inherently different, but we also found that certain properties have a strong dependence on the sampling windows length: we made experiments through computer simulations with various aggregation time windows and found that it has a great impact on the results.
In our presentation, we would like to briefly introduce the key findings of our previous results regarding to the elementary dynamic network models, and compare the theoretical results obtained from evaluating different empirical data sets. The selected data sets used for the comparison include political event data compiled from English-language news reports and a dataset created to analyze internet-mediated sexual encounters in Brazil.
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Comparison of Elementary Dynamic Network Models Using Empirical Data
1. Richárd O. Legéndi, László Gulyás
Eötvös Loránd University, Regional
Knowledge Centre
AITIA International, Inc,
rlegendi@aitia.ai, lgulyas@aitia.ai
Comparison of Elementary
Dynamic Network Models Using
Empirical Data
This work was partially supported by the European Union and the European Social
Fund through project FuturICT.hu (grant no.: TÁMOP-4.2.2.C-11/1/KONV-2012-0013).
TDN 2013, NetSci Satellite
Copenhagen, June 3-4, 2013
6. Elementary Dynamic Networks
Growing Networks
Shrinking Networks
Networks of Constant Size
Node set is fixed
Edge set (unweighted, undirected)
is changing about the same
constant size
7. Definitions
Snapshot network (@t)
The network at any single t moment in time.
(Using the finest possible granularity available in the model)
Cumulative network (@[t, t+T])
The union of snapshot networks
(collected over the specified interval of time)
Typically over the [0,T] interval in our studies
Summation network (@[t, t+T])
The sum of snapshot networks
(collected over the specified interval of time)
Typically yields multi-nets
9. Elementary Models of Dynamic
Networks (EDN’s)
Starting from an initial G0 network
ER1: Add each non-existing edge with pA. Delete
each existing edge with pD.
ER2: Add kA uniformly selected random new edges.
Delete kD existing edges.
SPA/CPA (Snapshot/Cumulative preferential):
Add kA edges from a random node with preferential
attachment based on the snapshot or cumulative
network. Delete kD existing edges.
AssortativeCPA/SPA Same as CPA/SPA, but
edges are added with assortative mixing.
DoubleCPA/SPA Same as CPA/SPA, but both
endpoints of an edge is chosen by weighted
selection
10. Elementary Dynamic Networks
We defined simple dynamic models
Similar in vein to models like:
Erdős-Rényi, Watts-Strogatz or Barabási-Albert
Starting from empty G0 networks (for the current
analysis)
Converging to the complete network
Explore various sampling windows
Through computer simulations
We compare snapshot and cumulative networks
15. The Gulf Dataset
The Gulf „dataset covers the states of the Gulf region
and the Arabian peninsula for the period 15 April 1979
to 31 March 1999. The Kansas Event Data System
used automated coding of English-language news
reports to generate political event data focusing on
the Middle East, Balkans, and West Africa. These
data are used in statistical early warning models to
predict political change. The ten-year project is based
in the Department of Political Science at the
University of Kansas; it has been funded primarily by
the U.S. National Science Foundation. There are two
versions of the data: a set coded from the lead
sentences only (57,000 events), and a set coded from
full stories (304,000 events)” 2013.06.03.TDN 2013 @ NetSci
The Kansas Event Data System: Gulf
data set
http://web.ku.edu/~keds/data.dir/gulf.ht
ml
16. The Gulf Dataset
2013.06.03.TDN 2013 @ NetSci
Connection of states within the Gulf region
Over 20 years
Annotated with imestamps
Preprocessed, both monthly-daily granularity
Relatively small network
174 nodes, 57 131 edges
Compared to similarly parameterized EDN runs
19. Sexual Network of Internet-Mediated
Prostitution
2013.06.03.TDN 2013 @ NetSci
„The community studied is a Brazilian, public
online forum with free registration that is financed
by advertisements. In this community, male
members grade and categorize their sexual
encounters with female escorts, both using
anonymous nicknames. The forum is oriented to
heterosexual males.”
Large, but sparse network
6,624 anonymous escorts and 10,106 sex buyers
50,632 edges
20. Preliminary Results
2013.06.03.TDN 2013 @ NetSci
• Density is increasing linearly
• Direct influence on other statistics
(# of edges, betweennes, avg. degree, etc.)
• Network is in the initial „evolution” phase
• Average path length starts decreasing far before becoming
connected
22. Summary
2013.06.03.TDN 2013 @ NetSci
We defined a set of models
Compared results to empirical data
Models show identical trends to the ones exposed in the
datasets
Gulf Dataset:
A highly connected core evolves in the network
(extremely high max. BC, clustering, but low avg. BC)
Granuality does not yield significant difference
Internet mediated sexual network:
Density is in the initial stage of evolution
Degree distribution is almost stable in the first 2000 turns, but
indication of change is in the last 200 steps
Preferential attachment plays a great role in real-world
systems
EDNs with PA are the closest to the data
23. Future Works
2013.06.03.TDN 2013 @ NetSci
Include studies of richer (more realistic?) EDN’s
Dedicating parts of the network as constant
More extensive studies (e.g., parameter
dependence)
24. Questions?
2013.06.03.TDN 2013 @ NetSci
THANK YOU!
Richárd O. Legéndi
http://people.inf.elte.hu/legendi/
June 3, 2013
This work was partially supported by the European Union and the European Social
Fund through project FuturICT.hu (grant no.: TÁMOP-4.2.2.C-11/1/KONV-2012-0013).