Graphlet-based characterization of many ego networks

Raphaël Charbey (1, 2, 3) , Christophe Prieur (2, 3)

1 Télécom ParisTech
2 I3 SES - Institut interdisciplinaire de l’innovation de Telecom Paris
3 SES - Département Sciences Economiques et Sociales

Network science gathers methods coming from various disciplines which sometimes hardly cross the boundaries between these disciplines. Widely used in molecular biology in the study of protein interaction networks, the enumeration, in a network, of all possible subgraphs of a limited size (usually around five nodes), often called graphlets, can only be found in a few works dealing with social networks. In the present work, we apply this approach to an original corpus of about 10 000 Facebook ego networks gathered from voluntary participants by a survey application. We define here an original measure that we call graphlet representativity, with which we produce a clustering of graphlets into five groups (paths, star-like, holes, light triangles, dense), along with an original visualization scheme for the comparison of ego networks. We then use the visu-alization in order to compare several clusterings of our corpus of networks, using various state-of-the art metrics. The graphlet representativity ends up producing the most dis-criminative clustering, so we describe the distinct structural characteristics of the five clusters of ego networks so obtained, and discuss the differences between 4-node and 5-node graphlets. We also provide many suggestions of followups of this work, both in sociology and in network science.

Domaines: Réseaux sociaux et d'information [cs.SI]; Ordinateur et société [cs.CY]; Recherche d'information [cs.IR]; Méthodes et statistiques

Raphaël Charbey, Christophe Prieur. Graphlet-based characterization of many ego networks. 2018. ⟨hal-01764253v2⟩