Multiple Partitioning of Multiplex Signed Networks

Nejat Arinik (1) , Rosa Figueiredo (1) , Vincent Labatut (1)

1 LIA - Laboratoire Informatique d'Avignon

In a signed graph, each link is associated to a sign, which can be either positive (+) or negative (−). This type of graph can be used to model any system containing two types of antithetical relationships (like/dislike, for/against, similar/different...). A signed graph is considered structurally balanced if it can be partitioned into two or more clusters, such that positive links are located inside the clusters, and negatives ones are in-between them. However, it is very rare for a real-world network to have a perfectly balanced structure : the question is how to quantify its imbalance. Various measures have been defined for this purpose, the simplest consisting in counting the numbers of misplaced links, i.e. negative ones located inside the groups, and positive ones located between them. Such measures are expressed relatively to a graph partition, so processing the graph balance amounts to identifying the partition corresponding to the lowest imbalance measure. In other words, calculating the graph balance can be formulated as an graph optimization problem. Our goal is to use this paradigm to study the roll-call voting activity of the Members of the European Parliament (MEPs) by bringing together three different disciplines : Operations Research, Social Science and Data Science. In this work, we want not only to detect groups of MEPs which would be cohesive in terms of votes, but also to identify the different characteristic voting patterns of the European Parliament (EP), i.e. the characteristic ways in which the MEP set is partitioned by these votes.

Mots clés: Graph Partitioning; European Parliament; Signed Graph; Correlation Clustering; Structural Balance

Domaines: Recherche opérationnelle [math.OC]; Réseaux sociaux et d'information [cs.SI]

Nejat Arinik, Rosa Figueiredo, Vincent Labatut. Multiple Partitioning of Multiplex Signed Networks. 21ème Congrès Annuel de la Société Française de Recherche Opérationnelle et d’Aide à la Décision (ROADEF), Société Française de Recherche Opérationnelle et d’Aide à la Décision, Feb 2020, Montpellier, France. ⟨hal-02428300⟩