کشف الگوی ساختاری فازی برای تحلیل گراف Discovering Fuzzy Structural Patterns for Graph Analytics

I. INTRODUCTION Nattributed graph contains attributed vertices connected by edges and each attributed vertex is associated with a set of attribute values. In these attributed graphs, there are a number of sub-graphs in which the vertices are more densely connected and are inter-related, according to their attribute values. Such sub-graphs are deemed as graph clusters, or communities, which are structural patterns in the graph. Many real-world problems can be formulated as the discovering of such clusters in the attributed graph. For example, in social network analysis, the identification of social groups is considered as social community detection. Similarly, the identification of functional modules in biological network graphs is also considered as cluster detection in biological graphs. To solve the problem of discovering clusters in graphs, several so-called graph clustering algorithms have been proposed. And the problem of clustering in graphs has drawn much attention in recent years [1] [2]. Unsurprisingly, most graph clustering algorithms detect clusters based on pre-specified topologies or edge structures. For example, in [3], an algorithm that detects clusters based on edge centrality is presented. In [4], another measure, called modularity, which is defined as a function of the differences in density within graph clusters and a null-graph (in which vertices are connected randomly) is proposed. Based on it, two algorithms presented in [5] and [6] attempt to detect graph clusters through modularity optimization. In [7], the authors present a formalism in which it shows that some clusters smaller than a certain size cannot be detected by those algorithms based on modularity optimization.