Introducing a mesoscopic scale with Conf luence in Modularity, to improve graph clustering resolution

Bruno Gaume (1) , Alexandre Delanoe , Alp Mestanogullari

1 CLLE-ERSS - Cognition, Langues, Langage, Ergonomie

Given a graph G = (V, E) and two vertices i, j ∈ V , we introduce Conf luence(G, i, j), a vertex mesoscopic closeness measure which brings together vertices from the same link-dense region of the graph G, and separates vertices coming from two distinct dense regions. Conf luence becomes a useful tool to avoid the resolution problems of the standard M odularity(G, Γ) measure for a given clustering Γ, as evidenced by our comparative study between these two measures on toy graphs. We additionally present a heuristic to nd a partitional clustering of a graph that tentatively optimizes a clustering quality function derived from Conf luence, comparing the new heuristic's behaviour to the state of the art Louvain and Inf omap methods on real terrain networks, while introducing a way to control the size of the resulting clusters along the way.

Domaines: Sciences de l'ingénieur [physics]

Bruno Gaume, Alexandre Delanoe, Alp Mestanogullari. Introducing a mesoscopic scale with Conf luence in Modularity, to improve graph clustering resolution. 2021. ⟨hal-03468437⟩