Currently, I am doing a Ph.D. at the Université Catholique de Louvain at
the group of Large Graphs and
Networks in the department of
mathematical engineering under the supervision of
Paul Van Dooren and
Yurii Nesterov. In 2008 I obtained my master degree in
sociology at the
University of Amsterdam. Fortunately I also have a background in mathematics and
computer science, otherwise I could probably forget about my Ph.D.
In general, I am interested in complex networks,
social influence (as in opinion dynamics
and the like), and conflict, topics where
hopefully math can meet the social sciences. I am currently working on a number of
different projects: (1) Resolution-limit-free community detection; (2)
Reputation and gossiping; and (3) Social event detection.
Resolution-limit-free detection of communities
Community detection in networks really took off when the measure called
'modularity' emerged in 2004. However, a few years later, it was found out
that it suffered from a very particular problem: a resolution limit. This
means the method is unable to detect small communities in large networks. So,
one of the suggestions was for example to detect subcommunities on each of the
communities you detect in the original graph. So, you need to `zoom in' on a
particular community, to find a more fine-grained substructure.
However, for long, it didn't remain exactly clear what this limit exactly
entailed, and more importantly: what the converse entailed. If there would be
a method that would not have this problem, what does it look like? And do such
methods exist?
In this project, we take a closer look to this resolution-limit, and define
rigorously the opposite: resolution-limit-free. The idea behind the definition of
resolution-limit-free is that, no matter what communities you will detect, you will
never have to `zoom in' to fined a more fine-grained substructure. So,
whatever partition you will have, it will not change when you look at any
communities separate from the rest of the network.
Using this definition, it is actually possible to show which type of methods
are resolution-limit-free. Amazingly, there seem to be only a few of such methods,
and can be easily described. More information can be found in
V.A. Traag,
P. Van Dooren,
Y. Nesterov,
Phys. Rev. E 84, 016114 (2011),
DOI:
10.1103/PhysRevE.84.016114.
Of course, you can also download
the source code of the algorithm.
Reputation and Gossip
In this project I am studying models for building reputation
from local interactions. Such models are useful for understanding how for
example cooperation can stabilize. Often it is assumed that people will
cooperate with someone who has a good reputation, treating the reputation as
an objective value. However, reputation will be constructed locally through
interactions. These interactions elicit gossip amongst people, sharing
information about a third party. Relevant questions here are whether such
gossiping models are evolutionary stable strategies; what type of interaction
patterns can emerge; how the amount of cooperation will evolve, et cetera.
Another, though related, approach is that of deciding on the
reputation of nodes in a given network. Whereas in the previous approach we
are looking from a dynamical point of view (how will relations of
cooperation change over time, and how will that affect the
reputation again), here we are looking from a more static point of view. Given
a certain network where people for example indicate whether they (dis)trust
each other, how should we reconstruct an accurate reputation? For
example, if somebody new arrives in the network, who could he trust best?
Social event detection
Concerts, football games, music festivals or even simply a birthday party in
the park: many people take part in various social events. But there's not much
knowledge about these social events: how many people typically
attend events; how often are there events; where do people come from to attend
events, et cetera. We are trying to detect such social events in massive
mobile phone data.
Such events can be characterized by the fact that there will be a large
gathering of people who would not be there normally. That is, most social
events will for most people constitute something out of their routine
behaviour. This then also hints at ways to analyze peoples' mobile behaviour
pattern.
This is a collaborative effort with Arnaud Browet,
Francesco Calabrese and
Frederic Morlot
International Relations
Many phenomena in international relations can be naturally modelled as
networks: trade networks, alliance networks, but also conflict networks.
Besides more traditional political science research, these networks have been
investigated for various characteristics such as the degree distribution, path
length, clustering, social balance, et cetera. We focus on partitioning the
network in multiple communities, where states within communities are better
connected to each other than to outside the community.
One research question for example focuses on the question whether trade
communities reduce conflict within those communities. Related issues such as
polarization in the international state system could also be studied using
such community partitions.
This is joint work with Yonatan Lupu
Source Code
You can find here the latest version of community detection software
implementing a number of features, most notable:
- Constant Potts Model (CPM) resolution free community detection
- Modularity optimization
- Reichardt-Bornholdt model with Erdos-Renyi null-model
- Dealing with negative links (i.e. with negative weights)
- Tuneable resolution parameters
- Multislice community detection
For more details on resolution-limit-free community detection, please refer to
V.A. Traag,
P. Van Dooren,
Y. Nesterov,
Phys. Rev. E 84, 016114 (2011),
DOI:
10.1103/PhysRevE.84.016114.
For community detection with negative links refer to
V. A. Traag and
Jeroen Bruggeman
Phys Rev E 80, 036115 (2009),
DOI:
10.1103/PhysRevE.80.036115
https://launchpad.net/louvain