Real-world bipartite communities tend to exhibit relaxed internal connectivity as their size increases, making traditional biclique models too restrictive for cohesive subgraph discovery. In this paper, we propose the Biflexi, a novel bipartite subgraph model that employs flexible, size-adaptive degree thresholds based on sublinear constraints. Our approach dynamically adjusts connectivity requirements according to subgraph size, enabling the discovery of larger and more realistic cohesive structures. We prove that the Maximum Biflexi problem is NP-hard and develop an efficient heuristic algorithm. Experimental results on real-world datasets demonstrate the effectiveness and scalability of our algorithm and the applicability of our model.

Cohesive subgraph discovery in hypergraphs is essential for analysing complex group interactions in various domains such as e-commerce, social media, and collaboration networks. However, existing models are vulnerable to large hyperedges that artificially inflate connectivity, obscuring meaningful structure. We propose the (k,s)-core, a new model requiring each node to have at least k neighbours with a minimum interaction strength s, measured via a size-sensitive decay function. This penalises noisy co-occurrences while preserving strong local patterns. We develop an efficient algorithm with theoretical guarantees, and experiments on real-world datasets demonstrate improved compactness and robustness over prior methods.

Community search in heterogeneous graphs is fundamental to applications such as expert team formation and scholarly collaboration. Many existing studies leverage meta-paths, which are sequences of node and edge types, to capture semantic relationships in heterogeneous graphs. However, most of them only consider the existence of meta-path instances, overlooking their frequency and thus failing to capture relationship strength. This limitation can result in communities that include nodes with numerous but weak relations. To capture the strength of relationships in heterogeneous graphs, we define the Strong Community (StrCom) model, which evaluates the strength between users based on the number of connecting meta-path instances. Building upon this model, we further propose the Budgeted Strong Community (BSC) problem by incorporating a size constraint. We provide theoretical analyses showing that the BSC problem is NP-hard and not in APX. To address this problem, we design three strategies-Shrink, Expand, and Hybrid-along with several optimization techniques to improve efficiency. Extensive experiments on large real-world datasets (e.g., DBLP, YAGO, DBpedia) demonstrate the effectiveness and efficiency of our approach. Specifically, our method achieves 3.49-107.09× higher PathSim scores for StrCom and two to five orders of magnitude higher scores for BSC compared to state-of-the-art baselines, demonstrating that the identified communities are both semantically coherent and structurally compact.

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.

Identifying cohesive subgraphs in hypergraphs is a fundamental problem that has received recent attention in data mining and engineering fields. Existing approaches mainly focus on a strongly induced subhypergraph or edge cardinality, overlooking the importance of the frequency of co-occurrence. In this paper, we propose a new cohesive subgraph named (k,g)-core, which considers both neighbour and co-occurrence simultaneously. The (k,g)-core has various applications including recommendation system, network analysis, and fraud detection. To the best of our knowledge, this is the first work to combine these factors. We extend an existing efficient algorithm to find solutions for (k,g)-core. Finally, we conduct extensive experimental studies that demonstrate the efficiency and effectiveness of our proposed algorithm.

Community Search, or finding a connected subgraph (known as a community) containing the given query nodes in a social network, is a fundamental problem. Most of the existing community search models only focus on the internal cohesiveness of a community. However, a high-quality community often has high modularity, which means dense connections inside communities and sparse connections to the nodes outside the community. In this paper, we conduct a pioneer study on searching a community with high modularity. We point out that while modularity has been popularly used in community detection (without query nodes), it has not been adopted for community search, surprisingly, and its application in community search (related to query nodes) brings in new challenges. We address these challenges by designing a new graph modularity function named Density Modularity. To the best of our knowledge, this is the first work on the community search problem using graph modularity. The community search based on the density modularity, termed as DMCS, is to find a community in a social network that contains all the query nodes and has high density-modularity. We prove that the DMCS problem is NP-hard. To efficiently address DMCS, we present new algorithms that run in log-linear time to the graph size. We conduct extensive experimental studies in real-world and synthetic networks, which offer insights into the efficiency and effectiveness of our algorithms. In particular, our algorithm achieves up to 8.5 times higher accuracy in terms of NMI than baseline algorithms.

Finding a set of co-clusters in a bipartite network is a fundamental and important problem. In this paper, we present the Attributed Bipartite Co-clustering (ABC) problem which unifies two main concepts: (i) bipartite modularity optimization, and (ii) attribute cohesiveness. To the best of our knowledge, this is the first work to find co-clusters while considering the attribute cohesiveness. We prove that ABC is NP-hard and is not in APX, unless P=NP. We propose three algorithms: (1) a top-down algorithm; (2) a bottom-up algorithm; (3) a group matching algorithm. Extensive experimental results on real-world attributed bipartite networks demonstrate the efficiency and effectiveness of our algorithms.

Searching for a community based on query nodes in a graph is a fundamental problem and has been extensively investigated. Most of the existing approaches focus on finding a community in a social network, and very few studies consider location-based social networks where users can check in locations. In this paper we propose the GeoSocial Community Search problem (GCS) which aims to find a social community and a cluster of spatial locations that are densely connected in a location-based social network simultaneously. The GCS can be useful for marketing and user/location recommendation. To the best of our knowledge, this is the first work to find a social community and a cluster of spatial locations that are densely connected from location-based social networks. We prove that the problem is NP-hard, and is not in APX, unless P = NP. To solve this problem, we propose three algorithms: core-based basic algorithm, top-down greedy removing algorithm, and an expansion algorithm. Finally, we report extensive experimental studies that offer insights into the efficiency and effectiveness of the proposed solutions.

With regard to social network analysis, we concentrate on two widely-accepted building blocks: community detection and graph drawing. Although community detection and graph drawing have been studied separately, they have a great commonality, which means that it is possible to advance one field using the techniques of the other. In this paper, we propose a novel community detection algorithm for undirected graphs, called BlackHole, by importing a geometric embedding technique from graph drawing. Our proposed algorithm transforms the vertices of a graph to a set of points on a low-dimensional space whose coordinates are determined by a variant of graph drawing algorithms, following the overall procedure of spectral clustering. The set of points are then clustered using a conventional clustering algorithm to form communities. Our primary contribution is to prove that a common idea in graph drawing, which is characterized by consideration of repulsive forces in addition to attractive forces, improves the clusterability of an embedding. As a result, our algorithm has the advantages of being robust especially when the community structure is not easily detectable. Through extensive experiments, we have shown that BlackHole achieves the accuracy higher than or comparable to the state-of-the-art algorithms.