Community Search (CS) is one of the fundamental tasks in network science and has attracted much attention due to its ability to discover personalized communities with a wide range of applications. Given any query nodes, CS seeks to find a densely connected subgraph containing query nodes. Most existing approaches usually study networks with a single type of proximity between nodes, which defines a single view of a network. However, in many applications such as biological, social, and transportation networks, interactions between objects span multiple aspects, yielding networks with multiple views, called multiplex networks. Existing CS approaches in multiplex networks adopt pre-defined subgraph patterns to model the communities, which cannot find communities that do not have such pre-defined patterns in real-world networks. In this paper, we propose a query-driven graph convolutional network in multiplex networks, CS-MLGCN, that can capture flexible community structures by learning from the ground-truth communities in a data-driven fashion. CS-MLGCN first combines the local query-dependent structure and global graph embedding in each type of proximity and then uses an attention mechanism to incorporate information on different types of relations. Experiments on real-world graphs with ground-truth communities validate the quality of the solutions we obtain and the efficiency of our model. CCS CONCEPTS• Computing methodologies → Neural networks; • Mathematics of computing → Graph algorithms.
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A key graph mining primitive is extracting dense structures from graphs, and this has led to interesting notions such as 𝑘-cores which subsequently have been employed as building blocks for capturing the structure of complex networks and for designing efficient approximation algorithms for challenging problems such as finding the densest subgraph. In applications such as biological, social, and transportation networks, interactions between objects span multiple aspects. Multilayer (ML) networks have been proposed for accurately modeling such applications. In this paper, we present FirmCore, a new family of dense subgraphs in ML networks, and show that it satisfies many of the nice properties of 𝑘-cores in single-layer graphs. Unlike the state of the art core decomposition of ML graphs, FirmCores have a polynomial time algorithm, making them a powerful tool for understanding the structure of massive ML networks. We also extend FirmCore for directed ML graphs. We show that FirmCores and directed FirmCores can be used to obtain efficient approximation algorithms for finding the densest subgraphs of ML graphs and their directed counterparts. Our extensive experiments over several real ML graphs show that our FirmCore decomposition algorithm is significantly more efficient than known algorithms for core decompositions of ML graphs. Furthermore, it returns solutions of matching or better quality for the densest subgraph problem over (possibly directed) ML graphs. CCS CONCEPTS• Mathematics of computing → Graph algorithms.
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.
We propose an information propagation model that captures important temporal aspects that have been well observed in the dynamics of fake news diffusion, in contrast with the diffusion of truth. The model accounts for differential propagation rates of truth and misinformation and for user reaction times. We study a time-sensitive variant of the misinformation mitigation problem, where k seeds are to be selected to activate a truth campaign so as to minimize the number of users that adopt misinformation propagating through a social network. We show that the resulting objective is non-submodular and employ a sandwiching technique by defining submodular upper and lower bounding functions, providing data-dependent guarantees. In order to enable the use of a reverse sampling framework, we introduce a weighted version of reverse reachability sets that captures the associated differential propagation rates and establish a key equivalence between weighted set coverage probabilities and mitigation with respect to the sandwiching functions. Further, we propose an offline reverse sampling framework that provides (1 - 1/ e - ϵ)-approximate solutions to our bounding functions and introduce an importance sampling technique to reduce the sample complexity of our solution. Finally, we show how our framework can provide an anytime solution to the problem. Experiments over five datasets show that our approach outperforms previous approaches and is robust to uncertainty in the model parameters.
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