Projects

Complex network analysis - projects 2019 19 décembre 2019

P1 : Local modularity selection for local community identification

A classical approach for local community identification relays on applying a greedy optimization approach that explore the network starting form the target node (for which we want to identify the community) and adding pro- gressively nodes that maximize a given quality function (ex. a local modula- rity function). One major short-come of this approach is that the computed community depends largely on the applied quality function and that all qua- lity functions can suffer from a problem of sticking into a local maxima.

In this project we want to explore the possibility of learning the best local modularity to apply in function of topological features of the target node.

The proposed approche is the following : given a set of networks for which a ground-truth information about the community structure is available, we compute for each node its local community applying different quality func- tions. Using the community ground truth information we can readily select the best quality function that yields the best result. Each node can be then be described by a vector of attributes given its different centralities values in the network.The problem of selecting the best quality function to apply can then be reformulated as multi-label supervised classification problem.

The goal of this project is to implement this approach using benchmark net- works (ex. Zachary Karate Club, Football, Dolphins, etc.) and also generated artificial networks (using namely the LFR graph generator (see : https ://- sites.google.com/site/andrealancichinetti/files) (https ://arxiv.org/abs/0805.4770)

P2 : Centrality-correlation based complex network similarity

Different work have showed that different centrality measures are diffe- rently correlated in different complex networks. Taking this fact into account, we propose the use of a centrality correlation profile, consisting of the values of the correlation coefficients between all pairs of centralities of interest, as a way to characterize networks. More precisely, we propose to apply rank-based correlation for measuring the correlation between the different centralities.

The proposed approach is the following : given a complex network of size n, and a set of k centrality measures C = {C

, . . . , C

}, we compute for each centrality C

the induced ranking vectors of the nodes σ

. For each couple of centrality measures C

, C

we can compute the raking correlation factor cor(σ

, σ

). A network N

can then be represented as a vector in the

1

k×(k−1)

2

dimensional space. Similarity betwenn two networks N

, N

can then be measured as the inverse of the distance separating both networks is the new representation space. The goal of this project is to implement the pro- posed network similarity measure and to evalute this approach by using this similarity measure to cluster networks generated using different network ge- nerators (Random network generators and the LFR generator (see : https ://- sites.google.com/site/andrealancichinetti/files) (https ://arxiv.org/abs/0805.4770)

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