FirmTruss Community Search in Multilayer Networks

Abstract

In applications such as biological, social, and transportation networks, interactions between objects span multiple aspects. For accurately modeling such applications, multilayer networks have been proposed. Community search allows for personalized community discovery and has a wide range of applications in large real-world networks. While community search has been widely explored for single-layer graphs, the problem for multilayer graphs has just recently attracted attention. Existing community models in multilayer graphs have several limitations, including disconnectivity, free-rider effect, resolution limits, and inefficiency. To address these limitations, we study the problem of community search over large multilayer graphs. We first introduce FirmTruss , a novel dense structure in multilayer networks, which extends the notion of truss to multilayer graphs. We show that FirmTrusses possess nice structural and computational properties and bring many advantages compared to the existing models. Building on this, we present a new community model based on FirmTruss, called FTCS , and show that finding an FTCS community is NP-hard. We propose two efficient 2-approximation algorithms, and show that no polynomial-time algorithm can have a better approximation guarantee unless P = NP. We propose an index-based method to further improve the efficiency of the algorithms. We then consider attributed multilayer networks and propose a new community model based on network homophily. We show that community search in attributed multilayer graphs is NP-hard and present an effective and efficient approximation algorithm. Experimental studies on real-world graphs with ground-truth communities validate the quality of the solutions we obtain and the efficiency of the proposed algorithms.

CS-TGN: Community Search via Temporal Graph Neural Networks

“…Datasets. We evaluate the performance of our proposed model using five real-world networks with ground-truth communities [1,4,20,22,50], from diverse domains, including social, communication, co-authorship, and brain networks. The statistics of these networks can be found in Table 1.…”

“…MLGCN [3] is a learningbased CS method in multiplex networks that leverages an attention mechanism to incorporate the information of different relation types. FTCS [4] finds the connected FirmTruss containing query nodes with the minimum diameter. In multiplex methods, each snapshot of the network is treated as one layer or view.…”

“…Since then, various community models have been proposed based on different pre-defined dense subgraphs [13], including 𝑘-core [40,41], 𝑘-truss [2,23], quasi-clique [11], 𝑘-plex [48], and densest subgraph [53]. Recently, community search has also been explored in directed [14,15], weighted [55], geo-social [21,56], multilayer [3,4,24], multi-valued [27], and labeled [12] graphs. Inspired by the success of Graph Neural Networks (GNNs), recently, several GNN-based approaches have been proposed for community search, such as [3,18,25].…”

“…Identifying communities is a fundamental problem in network science, where the aim is to partition a network into subgraphs that effectively capture dense groups of nodes with strong interconnections [16]. With the increasing focus on personalized communities, the query-dependent community discovery problem, known as community search (CS) [40], has become a popular area of research with a wide array of applications, including the classification of brain networks [4], modeling of social contagion [46], content recommendation [7], and team formation [17]. Given a graph and a set of query nodes, the CS problem aims to find a cohesive and dense subgraph containing the query nodes [40].…”