Abstract
The notion of $k$ -truss has been introduced a decade ago in social network analysis and security for community detection, as a form of cohesive subgraphs less stringent than a clique (set of pairwise linked nodes), and more selective than a k-core (induced subgraph with minimum degree $k$ ). A $k$ -truss is an inclusion-maximal subgraph $H$ in which each edge belongs to at least $k-2$ triangles inside $H$ . The truss decomposition establishes, for each edge $e$ , the maximum $k$ for which $e$ belongs to a $k$ -truss. Analogously to the largest clique and to the maximum $k$ -core, the strongest community for $k$ -truss is the max-truss, which corresponds to the $k$ -truss having the maximum $k$ . Even though the computation of truss decomposition and of the max-truss takes polynomial time, on a large scale, it suffers from handling a potentially cubic number of wedges. In this paper, we provide a new algorithm FMT, which advances the state of the art on different sides: lower execution time, lower memory usage, and no need for expensive hardware. We compare FMT experimentally with the most recent state-of-the-art algorithms on a set of large real-world and synthetic networks with over a billion edges. The massive improvement allows FMT to compute the max-truss of networks of tens of billions of edges on a single standard server machine.
Highlights
One of the most fundamental tasks in the analysis of real-world networks is that of community detection, which corresponds to identifying cohesive portions of a network according to some metrics
OUR CONTRIBUTION We address the problem of finding the k-trusses in large networks from a new angle by introducing algorithm FMT (G, M, r), which takes in input a graph G, plus two parameters that interplay with the performance of the algorithm:
WORKS In this paper, we have presented a new algorithm for computing k-trusses
Summary
One of the most fundamental tasks in the analysis of real-world networks is that of community detection, which corresponds to identifying cohesive portions of a network according to some metrics. Our execution time on real-world networks compares favorably with the most recent state-of-theart approaches for truss decomposition, coming from the GraphChallenge [23] and other papers on large real-world and synthetic graphs, as detailed, with only one solution (KM17) having slightly less space requirement per edge. FMT sensibly reduces the time and space required with respect to the truss decomposition, still computing exactly the max-truss In this way, we hope to shed further light on this popular community measure, both in its complexity and its relation to triangle density. At the same time, based on this knowledge, we provide scalable and efficient tools for computing the truss decomposition and the max-truss, which outperform known approaches and can process graphs with billions of edges in reasonable time and space. A preliminary version of the algorithm presented here was a finalist in the MIT Graph Challenge (graphchallenge. mit.edu/champions) and part of the contents of this paper appeared in [11]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
