Abstract
Discovering dense subgraphs in a graph is a fundamental graph mining task, which has a wide range of applications in social networks, biology and visualization to name a few. Even the problem of computing most cohesive subgraphs is NP-hard (like clique, quasi-clique, k-densest subgraph), there exists a polynomial time algorithm for computing the k-core and k-truss. In this paper, we propose a novel dense subgraph model, {mathsf {k}}-{mathsf {core}}-{mathsf {truss}}, which leverages on a new type of important edges based on the basis of k-core and k-truss. We investigate the structural properties of the {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} model. Compared to k-core and k-truss, {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} can significantly discover the interesting and important structural information out the scope of k-core and k-truss. We study two useful problems of {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} decomposition and {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} search. In particular, we develop a k-core-truss decomposition algorithm to find all {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} in a graph G by iteratively removing edges with the smallest {mathsf {degree}}-{mathsf {support}}. In addition, we offer a {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} search algorithm to identifying a particular {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} containing a given query node such that the core number k is the largest. Extensive experiments on several web-scale real-world datasets show the effectiveness and efficiency of {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} model and proposed algorithms.
Highlights
Graph model is widely used to represent connection relationships between entities in a wide variety of domains such as social and web networks, biology, communication networks, and so on [1]
Discovering dense subgraphs in a graph is a fundamental graph mining task, which has a wide range of applications in social networks, biology and visualization to name a few
We propose a novel dense subgraph model, k-core-truss, which leverages on a new type of important edges based on the basis of k-core and k-truss
Summary
Graph model is widely used to represent connection relationships between entities in a wide variety of domains such as social and web networks, biology, communication networks, and so on [1]. A k-truss of a graph G is the largest subgraph of G such that each edge is contained in at least k À 2 triangles in this subgraph. Given a parameter a [ 0, the importance of an edge e 1⁄4 ðu; vÞ in a graph G is defined as the maximum one between the value equaling to a times minimum degree of v and u, and the number of triangles containing e plus 2. The whole graph of 3-coretruss contains two overlapping subgraphs of 3-core and 3truss. – We conduct extensive experiments on five web-scale real-world datasets, and show that our k-core-truss algorithms can efficiently and effectively find cohesive substructures over real-world networks, which can significantly discover the interesting and important relationships out the scope of k-core and k-truss
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