Représentation d'un grand réseau à partir d'une classification hiérarchique de ses sommets

Fabrice Rossi (1) , Nathalie Villa-Vialaneix (1)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

Graph visualization is an important tool to understand the main features of a network but, when the number of nodes in the graph exceeds few hundreds, standard visualization methods are computationally expensive. Moreover, force directed algorithms do not help the understanding of the community structure of the newtork, if is exists. In this paper, a new visualization method based on a hierarchical clustering of the nodes of the graph is proposed. It can handle graphs having several thousands nodes in a few seconds. Several simplified representations of the graph are accessible, giving the user the opportunity to understand the macroscopic organization of the network and then, to focus on some particular parts of the graph. This refining process is controlled as follows. Partitions under consideration are evaluated via the classical modularity quality measure. A distribution of the quality measure in the case of graphs without structure is obtained by applying the proposed method to random graphs with the same degree distribution as the graph under study. Then only significant partitions are shown during the refining process. This approach is illustrated on several public datasets and compared with other visualization methods meant to emphasize the graph communities. It is also tested on a large network built from a corpus of medieval land charters.

Mots clés: Graphe; Visualisation; Classification; Clustering; MCMC

Domaines: Machine Learning [stat.ML]; Interface homme-machine [cs.HC]

Fabrice Rossi, Nathalie Villa-Vialaneix. Représentation d'un grand réseau à partir d'une classification hiérarchique de ses sommets. Journal de la Société Française de Statistique, 2011, 152 (3), pp.34-65. ⟨hal-00651577⟩