Finding Collections of k-Clique Percolated Components in Attributed Graphs Pierre-Nicolas Mougel 1,2 , Christophe Rigotti 1,2 , and Olivier Gandrillon 1,3 1 Universit´ e de Lyon, CNRS, INRIA 2 INSA-Lyon, LIRIS, UMR5205, F-69621, France 3 Universit´ e Lyon 1, CGPhiMC, UMR5534, F-69622, France Abstract. In this paper, we consider graphs where a set of Boolean at- tributes is associated to each vertex, and we are interested in k-clique percolated components (components made of overlapping cliques) in such graphs. We propose the task of finding the collections of homogeneous k- clique percolated components, where homogeneity means sharing a com- mon set of attributes having value true. A sound and complete algorithm based on subgraph enumeration is proposed. We report experiments on two real databases (a social network of scientific collaborations and a net- work of gene interactions), showing that the extracted patterns capture meaningful structures. Keywords: graph mining; network analysis; attributed graph; k-clique percolated component 1 Introduction During the last decade, graph mining has received an increasing interest in the data mining community. More recently, several works have considered the mining of enriched graphs where attributes are associated to the vertices. These works led to interesting results, for instance in clustering [4, 8, 15, 16], dense graph mining [7, 12] or graph matching [14]. In this paper, we focus on the special case where the domain of the attributes is Boolean and we propose to extract collections of components called k-clique percolated components [1]. More precisely, we define a pattern as a Collection of Homogeneous k-clique Percolated components (CoHoP), where homogeneity means that the vertices in all components share a common set of Boolean at- tributes having value true. A CoHoP pattern must also satisfy two additional constraints: it must contain more than a given number of k-clique percolated components and the vertices must have in common more than a given number of attributes set to true.A k-clique percolated component has been defined in [1] as a union of cliques of size k connected by overlaps of k - 1 vertices (we recall the more formal definition in the next section), and since then, it has been widely accept as one structure that can be used to represent the notion of community. A CoHoP, as introduced here, can thus be interpreted as a set of communities, where elements in all communities share similar Boolean properties.