Finding maximal stable cores in social networks

Maximal Stable Cores are a cohesive subgraph on a social network which use both engagement and similarity to identify stable groups of users. The problem is, when given a query user and a similarity threshold, to find all Maximal Stable Cores relative to the user. We propose a baseline algorithm and as the problem is NP-Hard, an improved heuristic algorithm which utilises linear time k-core decomposition. Experiments how that when the two algorithms differ, the improved algorithm significantly outperforms the baseline

Discovering strong communities with user engagement and tie strength

In this paper, we propose and study a novel cohesive subgraph model, named (k,s)-core, which requires each user to have at least k familiars or friends (not just acquaintances) in the subgraph. The model considers both user engagement and tie strength to discover strong communities. We compare the (k,s)-core model with k-core and k-truss theoretically and experimentally. We propose efficient algorithms to compute the (k,s)-core and decompose the graph by a particular sub-model k-fami. Extensive experiments show (1) our (k,s)-core and k-fami are effective cohesive subgraph models and (2) the (k,s)-core computation and k-fami decomposition are efficient on various real-life social networks

Efficient graph hierarchical decomposition with user engagement and tie strength

Graph decomposition methods using k-core and k-truss hierarchically group vertices and edges from external to internal by degrees of vertices or tie strength of edges. As both the user engagement of nodes and the strength of relationships are important, the (k,s)-core model is proposed in the literature to discover strong communities. Nevertheless, the decomposition algorithm regarding (k,s)-core is not yet investigated. In this paper, we propose (k,s)-core algorithms to decompose a graph into its hierarchical structures considering both user engagement and tie strength. We first present the basic (k,s)-core decomposition methods. Then, we propose the advanced algorithms DES and DEK which index the support of edges to enable higher-level cost-sharing in the peeling process. In addition, effective pruning strategies are applied to DES/DEK to further enhance performance. Moreover, we build a novel index based on the decomposition result and investigate an efficient (k,s)-core query algorithm based on our index. Extensive experimental evaluations on 12 real-world datasets verify the efficiency of our proposed decomposition algorithms and show that our index-based query algorithm can speed up the state-of-the-art query algorithms by up to three orders of magnitude

K-Connected Cores Computation in Large Dual Networks

Abstract Computing $$k\text {-}core$$ k-core s is a fundamental and important graph problem, which can be applied in many areas, such as community detection, network visualization, and network topology analysis. Due to the complex relationship between different entities, dual graph widely exists in the applications. A dual graph contains a physical graph and a conceptual graph, both of which have the same vertex set. Given that there exist no previous studies on the $$k\text {-}core$$ k-core in dual graphs, we formulate a k -connected core ($$k\text {-}CCO$$ k-CCO ) model in dual graphs. A $$k\text {-}CCO$$ k-CCO is a $$k\text {-}core$$ k-core in the conceptual graph, and also connected in the physical graph. Given a dual graph and an integer k, we propose a polynomial time algorithm for computing all $$k\text {-}CCO$$ k-CCO s. We also propose three algorithms for computing all maximum-connected cores ($$MCCO$$ MCCO ), which are the existing $$k\text {-}CCO$$ k-CCO s such that a $$(k+1)$$ (k+1) -$$CCO$$ CCO does not exist. We further study a subgraph search problem, which is computing a $$k\text {-}CCO$$ k-CCO that contains a set of query vertices. We propose an index-based approach to efficiently answer the query for any given parameter k. We conduct extensive experiments on six real-world datasets and four synthetic datasets. The experimental results demonstrate the effectiveness and efficiency of our proposed algorithms