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**Graphs: is there something between theory and practice?**Gilles Tredan*Vendredi 24 juin 2016 à 11h, salle 24-25/405***Temporal density of complex networks and ego-community dynamics**Sergey Kirgizov*Lundi 04 juillet 2016 à 11h, salle 24-25/405*Christophe Paul*Vendredi 08 juillet 2016 à 11h, salle 24-25/405*- affinity index algorithm analysis antipaedo attack bipartite blog network blogs capitalisme social Cascade centrality clustering communities community detection community structure complex network complex networks complex systems compression connected graphs data mining debian degree distribution degree peeling diameter diffusion diffusion phenomena distributed measurements DynamicNetworks dynamics edge-Markovian evolving graph eDonkey ego-centered ego-centered communities email epidemiology event detection evolving graphs evolving networks exploration failure fixed points formal concepts gossip graph graph algorithm graph decompositions Graphs hierarchical clustering honeypot influence influence ranking interaction networks internal links internet Internet topology intrinsic time IP-level ip exchanges lattice leaders link prediction long term communities markovian model measurement mesure d’influence metrics Metrology mobile networks Modelling modularity multi-ego-centered communities multi-scale multipartite graph network dynamics node proximity node similarity opinion dynamics outliers p2p P2P dynamics P2P networks parametric paris paris-traceroute path-vector routing pedophile activity phone power-law radar random graph random walks reachability robustness routing routing tables scale-free security simulation simulations sir social networks spreading spreading cascades stability statistical analysis stochastic process three-state cellular automata time-varying Topology traceroute triangles twitter UDP user profiles viral marketing visualization web wifi

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Louisa Harutyunyan.

Temporal density of complex networks and ego-community dynamics

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.