Core decomposition in large temporal graphs

Wu, Huanhuan; Cheng, James; Lu, Yi; Ke, Yiping; Huang, Yuzhen; Yan, Da; Wu, Hejun

doi:10.1109/bigdata.2015.7363809

Cited by 64 publications

(35 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…k-dense triangle k-core k-truss k-community k-truss community k-(2,3) nucleus them efficiently in the external memory computation model is not a trivial problem and will limit the performance of proposed algorithms for finding k-core subgraphs and constructing the hierarchy. Similar argument can be considered for weighted [19], probabilistic [6], and temporal [52] k-core decompositions, all of which have some kind of thresholdbased adaptations on weights, probabilities and timestamps, respectively. On the other hand, connectedness definition is semantically unclear for some existing works like the directed graph core decomposition [18].…”

Section: K-core Decompositionmentioning

confidence: 99%

“…In the original definition of k-core, Seidman states that k-core is the maximal and connected subgraph where any vertex has at least degree k [43]. However, almost all the recent papers on k-core algorithms [8,18,19,6,36,32,28,52,51,32] did not mention that k-core is a connected subgraph although they cite Seidman's seminal work [43]. On the k-truss side, the idea is introduced independently by Saito et al [39] (as k-dense), Cohen [10] (as k-truss), Zhang and Parthasarathy [56] (as triangle k-core), and Verma and Butenko [47] (as k-community).…”

Section: Problem Misconception and Challengesmentioning

confidence: 99%

See 1 more Smart Citation

Fast hierarchy construction for dense subgraphs

Sarıyüce

Pınar

2016

Proc. VLDB Endow.

View full text Add to dashboard Cite

Discovering dense subgraphs and understanding the relations among them is a fundamental problem in graph mining. We want to not only identify dense subgraphs, but also build a hierarchy among them (e.g., larger but sparser subgraphs formed by two smaller dense subgraphs). Peeling algorithms (k-core, k-truss, and nucleus decomposition) have been effective to locate many dense subgraphs. However, constructing a hierarchical representation of density structure, even correctly computing the connected k-cores and k-trusses, have been mostly overlooked. Keeping track of connected components during peeling requires an additional traversal operation, which is as expensive as the peeling process. In this paper, we start with a thorough survey and point to nuances in problem formulations that lead to significant differences in runtimes. We then propose efficient and generic algorithms to construct the hierarchy of dense subgraphs for k-core, k-truss, or any nucleus decomposition. Our algorithms leverage the disjoint-set forest data structure to efficiently construct the hierarchy during traversal. Furthermore, we introduce a new idea to avoid traversal. We construct the subgraphs while visiting neighborhoods in the peeling process, and build the relations to previously constructed subgraphs. We also consider an existing idea to find the k-core hierarchy and adapt for our objectives efficiently. Experiments on different types of large scale real-world networks show significant speedups over naive algorithms and existing alternatives. Our algorithms also outperform the hypothetical limits of any possible traversal-based solution.

show abstract

Section: K-core Decompositionmentioning

confidence: 99%

Section: Problem Misconception and Challengesmentioning

confidence: 99%

Fast hierarchy construction for dense subgraphs

Sarıyüce

Pınar

2016

Proc. VLDB Endow.

View full text Add to dashboard Cite

show abstract

“…In [157], the definition of the core decomposition is adapted to the case of temporal graphs. The concept of (k, h)-core is defined, where as usual k represents the degree of a node and h represents the number of multiple temporal edges between two vertices.…”

Section: Temporal Graphsmentioning

confidence: 99%

“…• 2005 • network analysis [8], visualization [6] • 2006 • complex networks [41], fingerprinting and visualization [7] • 2007 • internet topology [29] truss decomposition [34] • 2008 • internet evolution [165], network analysis [69,87,9], neuroscience [67] • 2009 • cell biology [99] • 2010 • influential spreaders [79] D-cores [62], disk-based computation [32], distributed computation [109], anchored k-core [20] • 2011 • communities [63], influence [28], neuroscience [147] triangle cores (truss) [150,166], weighted networks [54] • 2012 • visualizing triangle k-core [166] dynamic cores [127], distributed computation [110] , weighted networks [43] • 2013 • influential spreaders [168], engagement [103,55], network analysis [1], neuroscience [135] local estimation [114], uncertain graphs [24], S-cores [60] • 2014 • clustering [61], neuroscience [125], influential spreaders [119,95] temporal graphs [157], disk-based and in-memory [77], parallel computation [134], density-friendly decomposition…”

Section: Introductionmentioning

confidence: 99%

The core decomposition of networks: theory, algorithms and applications

et al. 2019

View full text Add to dashboard Cite

The core decomposition of networks has attracted significant attention due to its numerous applications in real-life problems. Simply stated, the core decomposition of a network (graph) assigns to each graph node v, an integer number c(v) (the core number), capturing how well v is connected with respect to its neighbors. This concept is strongly related to the concept of graph degeneracy, which has a long history in Graph Theory. Although the core decomposition concept is extremely simple, there is an enormous interest in the topic from diverse application domains, mainly because it can be used to analyze a network in a simple and concise manner by quantifying the significance of graph nodes. Therefore, there exists a respectable number of research works that either propose efficient algorithmic techniques under different settings and graph types or apply the concept to another problem or scientific area. Based on this large interest in the topic, in this survey, we perform an in-depth discussion of core decomposition, focusing mainly on: i) the basic theory and fundamental concepts, ii) the algorithmic techniques proposed for computing it efficiently under different settings, and iii) the applications that can benefit significantly from it.

show abstract

“…They characterize cores on 2-layer Erdős-Rényi and 2-layer scale-free networks, then they analyze real-world (2-layer) air-transportation networks. A type of core decomposition for temporal networks has been proposed by Wu et al [30], who define the (k, h)-core as the largest subgraph in which every vertex has at least k neighbors and at least h temporal connections with each of them. Finally, Zhang et al [31] study the problem of enumerating all maximal cores of a (non-temporal) variant of core decomposition, that turns out to be NP-hard.…”

Section: State Of the Artmentioning

confidence: 99%

Cores and Other Dense Structures in Complex Networks

Galimberti

2019

Companion Proceedings of the 2019 World Wide Web Conference

View full text Add to dashboard Cite

Complex networks are a powerful paradigm to model complex systems. Specific network models, e.g., multilayer networks, temporal networks, and signed networks, enrich the standard network representation with additional information to better capture real-world phenomena. Despite the keen interest in a variety of problems, algorithms, and analysis methods for these types of network, the problem of extracting cores and dense structures still has unexplored facets.In this work, we present advancements to the state of the art by the introduction of novel definitions and algorithms for the extraction of dense structures from complex networks, mainly cores. At first, we define core decomposition in multilayer networks together with a series of applications built on top of it, i.e., the extraction of maximal multilayer cores only, densest subgraph in multilayer networks, the speed-up of the extraction of frequent cross-graph quasi-cliques, and the generalization of community search to the multilayer setting. Then, we introduce the concept of core decomposition in temporal networks; also in this case, we are interested in the extraction of maximal temporal cores only. Finally, in the context of discovering polarization in large-scale online data, we study the problem of identifying polarized communities in signed networks.The proposed methodologies are evaluated on a large variety of real-world networks against naïve approaches, non-trivial baselines, and competing methods. In all cases, they show effectiveness, efficiency, and scalability. Moreover, we showcase the usefulness of our definitions in concrete applications and case studies, i.e., the temporal analysis of contact networks, and the identification of polarization in debate networks.

show abstract

Core decomposition in large temporal graphs

Cited by 64 publications

References 18 publications

Fast hierarchy construction for dense subgraphs

Fast hierarchy construction for dense subgraphs

The core decomposition of networks: theory, algorithms and applications

Cores and Other Dense Structures in Complex Networks

Contact Info

Product

Resources

About