Lundi 04 julliet 2016 à 11h, salle 24-25/405

**Abstract**

At first, we say that a ego-community structure is a probability
measure defined on the set of network nodes. Any subset of nodes may
engender its own ego-community structure around. Many community
detection algorithms can be modified to yield a result of this type,
for instance, the personalized pagerank. We also recall that
community detection algorithms (including personalized pagerank) can
be viewed from different perspectives: random walks, convergence of
markov chain, spectral clustering, optimization, mincut(s), discrete
cheeger inequality(ies), etc.
Next, we present a continuous version of Viard-Latapy-Magnien link
streams, that we call "temporal density". Classical kernel density
estimation is used to move from discrete link streams towards their
continuous counterparts. Using matrix perturbation theory we can prove
that ego-community structure changes smoothly when the network evolves
smoothly. This is very important, for example, for visualization
purposes.
Combining the temporal density and personalized pagerank methods, we
are able to visualize and study the evolution of the ego-community
structures of complex networks with a large number of temporal links
in order to extract interacting information. For example, we can
detect events, trace the evolution of (ego-)community structure, etc.
We illustrate and validate our approach using "Primary school temporal
network data" provided by sociopatterns.org, and we show how the
temporal density can be applied to the study of very large datasets,
such as a collection of tweets written by European Parliament
candidates during European Parliament election in 2014.