Listing all k -cliques in a graph is a fundamental graph mining problem that finds many important applications in community detection and social network analysis. Unfortunately, the problem of k -clique listing is often deemed infeasible for a large k , as the number of k -cliques in a graph is exponential in the size k. The state-of-the-art solutions for the problem are based on the ordering heuristics on nodes which can efficiently list all k -cliques in large real-world graphs for a small k (e.g., k ≤ 10). Even though a variety of heuristic algorithms have been proposed, there still lacks a thorough comparison to cover all the state-of-the-art algorithms and evaluate their performance using diverse real-world graphs. This makes it difficult for a practitioner to select which algorithm should be used for a specific application. Furthermore, existing ordering based algorithms are far from optimal which might explore unpromising search paths in the k -clique listing procedure. To address these issues, we present a comprehensive comparison of all the state-of-the-art k -clique listing and counting algorithms. We also propose a new color ordering heuristics based on greedy graph coloring techniques which is able to significantly prune the unpromising search paths. We compare the performance of 14 various algorithms using 17 large real-world graphs with up to 3 million nodes and 100 million edges. The experimental results reveal the characteristics of different algorithms, based on which we provide useful guidance for selecting appropriate techniques for different applications.
The higher-order structure cohesive subgraph mining is an important operator in many graph analysis tasks. Recently, the colorful h -star core model has been proposed as an effective alternative to h -clique based cohesive subgraph models, in consideration of both efficiency and utilities in many practical applications. The existing peeling algorithms for colorful h -star core decomposition are to iteratively delete a node with the minimum colorful h -star degree. Hence, these methods are inherently sequential and suffer from two limitations: low parallelism and inefficiency for dynamic graphs. To enable high-performance colorful h -star core decomposition in large-scale graphs, we propose highly parallelizable local algorithms based on a novel concept of colorful h -star n -order H-index and conduct thorough analyses for its properties. Moreover, three optimizations have been developed to further improve the convergence performance. Based on our local algorithm and its optimized variants, we can efficiently maintain colorful h -star cores in dynamic graphs. Furthermore, we design lower and upper bounds for core numbers to facilitate identifying unaffected nodes in presence of graph updates. Extensive experiments conducted on 14 large real-world datasets with billions of edges demonstrate that our proposed algorithms achieve a 10 times faster convergence speed and a three orders of magnitude speedup when handling graph changes.
No abstract
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.