Alexis Baudin

Community detection is a popular approach to understand the organization of interactions in static networks. For that purpose, the Clique Percolation Method (CPM), which involves the percolation of k-cliques, is a well-studied technique that offers several advantages. Besides, studying interactions that occur over time is useful in various contexts, which can be modeled by the link stream formalism. The Dynamic Clique Percolation Method (DCPM) has been proposed for extending CPM to temporal networks. However, existing implementations are unable to handle massive datasets. We present a novel algorithm that adapts CPM to link streams, which has the advantage that it allows us to speed up the computation time with respect to the existing DCPM method. We evaluate it experimentally on real datasets and show that it scales to massive link streams. For example, it allows to obtain a complete set of communities in under twenty-five minutes for a dataset with thirty million links, what the state of the art fails to achieve even after a week of computation. We further show that our method provides communities similar to DCPM, but slightly more aggregated. We exhibit the relevance of the obtained communities in real world cases, and show that they provide information on the importance of vertices in the link streams.

Link streams offer a good model for representing interactions over time. They consist of links (b,e,u,v), where u and v are vertices interacting during the whole time interval [b,e]. In this paper, we deal with the problem of enumerating maximal cliques in link streams. A clique is a pair (C,[t0,t1]), where C is a set of vertices that all interact pairwise during the full interval [t0,t1]. It is maximal when neither its set of vertices nor its time interval can be increased. Some of the main works solving this problem are based on the famous Bron-Kerbosch algorithm for enumerating maximal cliques in graphs. We take this idea as a starting point to propose a new algorithm which matches the cliques of the instantaneous graphs formed by links existing at a given time t to the maximal cliques of the link stream. We prove its validity and compute its complexity, which is better than the state-of-the art ones in many cases of interest. We also study the output-sensitive complexity, which is close to the output size, thereby showing that our algorithm is efficient. To confirm this, we perform experiments on link streams used in the state of the art, and on massive link streams, up to 100 million links. In all cases our algorithm is faster, mostly by a factor of at least 10 and up to a factor of 104. Moreover, it scales to massive link streams for which the existing algorithms are not able to provide the solution.

Les flots de liens offrent un formalisme de description d’interactions au cours du temps. Un lien correspond à deux sommets qui interagissent sur un intervalle de temps. Une clique est un ensemble de sommets associé à un intervalle de temps durant lequel ils sont tous connectés. Elle est maximale si ni son ensemble de sommets ni son intervalle de temps ne peuvent être augmentés. Les algorithmes existants pour énumérer ces structures ne permettent pas de traiter des jeux de données réels de plus de quelques centaines de milliers d’interactions. Or, l’accès à des données toujours plus massives demande d’adapter les outils à de plus grandes échelles. Nous proposons alors un algorithme qui énumère les cliques maximales sur des réseaux temporels réels et massifs atteignant jusqu’à plus de 100 millions de liens. Nous montrons expérimentalement qu’il améliore l’état de l’art de plusieurs ordres de grandeur.