Mining Graph Topological Patterns: Finding Covariations among Vertex Descriptors

Abstract

In this article, we propose to mine the graph topology of a large attributed graph by finding regularities among vertex descriptors. Such descriptors are of two types: (1) the vertex attributes that correspond to the information conveyed by the vertices themselves and (2) some topological properties, used to describe the connectivity of each vertex in the graph. Such topological properties and attributes are mostly of numerical or ordinal types and their similarity can be captured by quantifying their co-variation, that is, if their largest or smallest values are supported mostly by the same set of vertices. A topological pattern is thus defined as a set of vertex attributes and topological properties that strongly co-vary over the vertices of the graph. Such pattern mining task relies on frequent pattern mining and graph topology analysis to reveal the links that exist between the relation encoded by the graph and the vertex attributes. For instance, a topological pattern in a co-authorship graph, where vertices represent authors, edges encode coauthorship, and vertex attributes reveal the number of publications in several journals, could be "the higher the number of publications in IEEE TKDE, the higher the closeness centrality of the vertex within the graph". Hence, such pattern discloses the fact that the number of times an author publishes at IEEE TKDE is positively correlated to the fact she has co-authored papers with other central authors, inducing a rather short distance to other graph vertices. We propose several interestingness measures of topological patterns that are different w.r.t. the pairs of vertices considered while evaluating up and down co-variations between properties and attributes: (1) considering all the pairs of vertices enables to find patterns that are true all over the graph; (2) taking into account only the vertex pairs that are in a specific order w.r.t. a selected attribute reveals the topological patterns that emerge with respect to this attribute; (3) examining the vertex pairs that are connected in the graph makes it possible to identify patterns that are structurally correlated to the relationship encoded by the graph. An efficient algorithm that combines searching and pruning strategies in the identification of the most relevant topological patterns is presented. Besides a classical empirical study, we report case studies on four real-life networks showing that our approach provides valuable knowledge in a feasible time.

What effects topological changes in dynamic graphs?

“…Following the same motivation, Sese et al [29] extract (not necessarily dense) subgraph with common itemsets. In [27], the authors propose to mine the graph topology of a large attributed graph by finding regularities among vertex descriptors that are of two types: vertex attributes and topological properties.…”

Triggering patterns of topology changes in dynamic graphs

“…For instance, the degree describes the close neighborhood of a vertex, and centrality measures depict the role of the vertex in the whole graph [23], that is to say its connectivity with respect to all other vertices. Our goal is to highlight how variations of attribute values of a vertex can later impact on its connectivity.…”

“…Following the same motivation, Sese et al [25] extract (not necessarily dense) subgraph with common itemsets. In [23], the authors propose to mine the graph topology of a large attributed graph by finding regularities among vertex descriptors.…”

Mining Maximal Quasi Regular Patterns in Weighted Dynamic Networks

“…A novel method [11] for graph clustering based on both structural and attribute similarities through a unified distance measure has been proposed in 2009 of an efficient algorithm [12] for the NP-Hard problem of finding the highest-scoring temporal sub graph in a dynamic network. In 2013, a paper [13] focusing on mining the graph topology of a large attributed graph by finding irregularities among vertex descriptors and analyzing the resulting topological patterns using three measures has also been brought forward. However, due to the ever increasing rate of data, the problem of noise/jitter has surfaced.…”