Identifying cohesive subgraphs within networks is a fundamental problem in graph theory, relevant to various domains. The traditional clique problem, which finds fully connected subgraphs, often faces limitations due to its strict connectivity requirements. This paper introduces a novel degree-based relaxation model called Flexi-clique, where the degree constraint is adjusted sub-linearly based on the subgraph size. We establish that the maximum Flexi-clique problem is NP-hard and propose an efficient and effective peeling algorithm to address it. Our extensive experimental evaluation of real-world datasets demonstrates the effectiveness and efficiency of our approach in discovering large, cohesive subgraphs in networks.

The creative web is all about combining different types of media to create a unique and engaging online experience. Multimodal data, such as text and images, is a key component in the creative web. Social media posts that incorporate both text descriptions and images offer a wealth of information and context. Text in social media posts typically relates to one topic, while images often convey information about multiple topics due to the richness of visual content. Despite this potential, many existing multimodal topic models do not take these criteria into account, resulting in poor quality topics being generated. Therefore, we proposed a Coherent Topic modeling for Multimodal Data (CTM-MM), which takes into account that text in social media posts typically relates to one topic, while images can contain information about multiple topics. Our experimental results show that CTM-MM outperforms traditional multimodal topic models in terms of classification and topic coherence.

As location-based services using mobile devices have become globally popular these days, social network analysis (especially, community detection) increasingly benefits from combining social relationships with geographic preferences. In this regard, this article addresses the emerging problem of geosocial community detection. We first formalize the problem of geosocial co-clustering , which co-clusters the users in social networks and the locations they visited. Geosocial co-clustering detects higher-quality communities than existing approaches by improving the mapping clusterability , whereby users in the same community tend to visit locations in the same region. While geosocial co-clustering is soundly formalized as non-negative matrix tri-factorization , conventional matrix tri-factorization algorithms suffer from a significant computational overhead when handling large-scale datasets. Thus, we also develop an efficient framework for geosocial co-clustering, called GEOsocial COarsening and DEcomposition (GEOCODE) . To achieve efficient matrix tri-factorization, GEOCODE reduces the numbers of users and locations through coarsening and then decomposes the single whole matrix tri-factorization into a set of multiple smaller sub-matrix tri-factorizations. Thorough experiments conducted using real-world geosocial networks show that GEOCODE reduces the elapsed time by 19–69 times while achieving the accuracy of up to 94.8% compared with the state-of-the-art co-clustering algorithm. Furthermore, the benefit of the mapping clusterability is clearly demonstrated through a local expert recommendation application.

This paper proposes LinkBlackHole*, a novel algorithm for finding communities that are (i) overlapping in nodes and (ii) mixing (not separating clearly) in links. There has been a small body of work in each category, but this paper is the first one that addresses both. For this purpose, LinkBlackHole* incorporates the advantages of both the link-space transformation and the black hole transformation. Thorough experiments show superior quality of the communities detected by LinkBlackHole* to those detected by other state-of-the-art algorithms.

This paper proposes LinkBlackHole*, a novel algorithm for finding communities that are (i) overlapping in nodes and (ii) mixing (not separating clearly) in links. There has been a small body of work in each category, but this paper is the first one that addresses both. LinkBlackHole* is a merger of our earlier two algorithms, LinkSCAN* and BlackHole, inheriting their advantages in support of highly-mixed overlapping communities. The former is used to handle overlapping nodes, and the latter to handle mixing links in finding communities. Like LinkSCAN and its more efficient variant LinkSCAN*, this paper presents LinkBlackHole and its more efficient variant LinkBlackHole*, which reduces the number of links through random sampling. Thorough experiments show superior quality of the communities detected by LinkBlackHole* and LinkBlackHole to those detected by other state-of-the-art algorithms. In addition, LinkBlackHole* shows high resilience to the link sampling effect, and its running time scales up almost linearly with the number of links in a network.

Amulti-layer graphconsists of multiple layers of weighted graphs, where the multiple layers represent the different aspects of relationships. Considering multiple aspects (i.e., layers) together is essential to achieve a comprehensive and consolidated view. In this article, we propose a novel framework ofdifferential flattening, which facilitates the analysis of multi-layer graphs, and apply this framework to community detection. Differential flattening merges multiple graphs into a single graph such that the graph structure with the maximum clustering coefficient is obtained from the single graph. It has two distinct features compared with existing approaches. First, dealing with multiple layers is doneindependentlyof a specific community detection algorithm, whereas previous approaches rely on a specific algorithm. Thus, any algorithm for a single graph becomes applicable to multi-layer graphs. Second, the contribution of each layer to the single graph is determinedautomaticallyfor the maximum clustering coefficient. Since differential flattening is formulated by an optimization problem, the optimal solution is easily obtained by well-known algorithms such as interior point methods. Extensive experiments were conducted using the Lancichinetti-Fortunato-Radicchi (LFR) benchmark networks as well as the DBLP, 20 Newsgroups, and MIT Reality Mining networks. The results show that our approach of differential flattening leads to discovery of higher-quality communities than baseline approaches and the state-of-the-art algorithms.