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Listing All Maximal k-Plexes in Temporal Graphs [article]

Matthias Bentert, Anne-Sophie Himmel, Hendrik Molter, Marco Morik, Rolf Niedermeier, René Saitenmacher
2019 arXiv   pre-print
We develop a recursive algorithm for enumerating all maximal Δ-k-plexs and perform experiments on real-world social networks that demonstrate the practical feasibility of our approach.  ...  We define a Δ-k-plex as a set of vertices and a time interval, where during this time interval each vertex has in each consecutive Δ + 1 time steps at least one edge to all but at most k-1 vertices in  ...  [43] and the fastest algorithm for listing all maximal k-plexes in a static graph is due to Berlowitz et al. [4] .  ... 
arXiv:1806.10210v4 fatcat:f27onlnu7za55dmum6ui6kycpi

Enumerating Maximal k-Plexes with Worst-Case Time Guarantee

Yi Zhou, Jingwei Xu, Zhenyu Guo, Mingyu Xiao, Yan Jin
To our best knowledge, for the first time, FaPlexen lists all maximal k-plexes with provably worst-case running time O(n2γn) in a graph with n vertices, where γ < 2.  ...  Hence, k-plex, a subgraph in which any vertex is adjacent to all but at most k vertices, is introduced as a relaxation of clique.  ...  Given an undirected graph G = (V, E), a positive integer k, list all the maximal k-plexes induced from G.  ... 
doi:10.1609/aaai.v34i03.5625 fatcat:csv6kynf4vgdlfm26fzfn2akli

Efficient Algorithms to Mine Maximal Span-Trusses From Temporal Graphs [article]

Quintino Francesco Lotito, Alberto Montresor
2020 arXiv   pre-print
In this paper, we introduce the concept of (k, Δ)-truss (span-truss) in temporal graphs, a temporal generalization of the k-truss, in which k captures the information about the density and Δ captures the  ...  temporal graphs.  ...  Algorithm 2 Maximal span-trusses Input: A temporal graph = ( , , ). Output: The set of all maximal span-trusses of .  ... 
arXiv:2009.01928v2 fatcat:bvurwfyrcfdznfltdgcsmodo2i

Core and periphery structures in protein interaction networks

Feng Luo, Bo Li, Xiu-Feng Wan, Richard H Scheuermann
2009 BMC Bioinformatics  
We find that the k-plex cores consist of either "party" proteins, "date" proteins, or both.  ...  Then, computational methods are proposed to identify two types of cores, k-plex cores and star cores, from PINs.  ...  In this study, we define a core in a PIN as a local maximal k-plex with k ≤ n/2 , where n is the number of nodes in the sub-graph.  ... 
doi:10.1186/1471-2105-10-s4-s8 pmid:19426456 pmcid:PMC2681073 fatcat:cqyl3ko6yfcmdjccbgxq4iacla

An Exact Algorithm for Maximum k-Plexes in Massive Graphs

Jian Gao, Jiejiang Chen, Minghao Yin, Rong Chen, Yiyuan Wang
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
The aim of this paper is to propose a novel exact k-plex algorithm that can deal with large-scaled graphs with millions of vertices and edges.  ...  The maximum k-plex, a generalization of maximum clique, is used to cope with a great number of real-world problems.  ...  We say a k-plex is maximal if any other k-plex cannot strictly contain it. The maximum k-plex problem is to find the k-plex with the largest size of a given graph.  ... 
doi:10.24963/ijcai.2018/201 dblp:conf/ijcai/GaoCYCW18 fatcat:xuvfet5otrajdox747d427plb4

In Search of the Densest Subgraph

András Faragó, Zohre R. Mojaveri
2019 Algorithms  
In this survey paper, we review various concepts of graph density, as well as associated theorems and algorithms.  ...  Our goal is motivated by the fact that, in many applications, it is a key algorithmic task to extract a densest subgraph from an input graph, according to some appropriate definition of graph density.  ...  Listing All Maximal Cliques While finding a maximum clique is hard, listing all inclusion-wise maximal cliques, which, of course, include all maximum (notice the difference in word usage: maximum refers  ... 
doi:10.3390/a12080157 fatcat:7rht55sor5errh2zkyvildkmhi

Algorithmic Enumeration: Output-sensitive, Input-Sensitive, Parameterized, Approximativ (Dagstuhl Seminar 18421)

Henning Fernau, Petr. A. Golovach, Marie-France Sagot, Michael Wagner
2019 Dagstuhl Reports  
Enumeration problems require to list all wanted objects of the input as, e.g., particular subsets of the vertex or edge set of a given graph or particular satisfying assignments of logical expressions.  ...  areas, in particular Biology.  ...  Listing All Maximal k-Plexes in Temporal Graphs We define a ∆-k-plex as a set of vertices with a lifetime, where during the lifetime each vertex has an edge to all but at most k − 1 vertices at least once  ... 
doi:10.4230/dagrep.8.10.63 dblp:journals/dagstuhl-reports/FernauGS18 fatcat:dwb3bv2onzanvgh6ucxh6atswm

A Survey of Community Search Over Big Graphs [article]

Yixiang Fang, Xin Huang, Lu Qin, Ying Zhang, Wenjie Zhang, Reynold Cheng, Xuemin Lin
2019 arXiv   pre-print
Consequently, how to efficiently find high-quality communities from big graphs is an important research topic in the era of big data.  ...  With the rapid development of information technologies, various big graphs are prevalent in many real applications (e.g., social media and knowledge bases).  ...  Acknowledgments We would like to thank Jiafeng Hu *For lack of space, we use abbreviations for the names of major conferences and journals in database and data mining areas (e.g., we use "PVLDB" to mean  ... 
arXiv:1904.12539v2 fatcat:swx7eervgbbgxpcf6znkx6cne4

Enumerating Isolated Cliques in Temporal Networks [article]

Hendrik Molter and Rolf Niedermeier and Malte Renken
2019 arXiv   pre-print
Motivated by recent work on enumerating cliques in temporal networks, we lift the isolation concept to this setting.  ...  Herein, a clique is considered isolated if it has few edges connecting it to the rest of the graph.  ...  In particular, there are numerous approaches (both from a more theoretical and from a more heuristic side) for listing all maximal cliques (that is, fully-connected subgraphs) in a graph. 1 It is well-known  ... 
arXiv:1909.06292v2 fatcat:iylnyllvuzbmdiijsxmg32slzy

On social-temporal group query with acquaintance constraint

De-Nian Yang, Yi-Ling Chen, Wang-Chien Lee, Ming-Syan Chen
2011 Proceedings of the VLDB Endowment  
with most of the members in the group, and (3) selecting an activity period available for all attendees.  ...  Therefore, this paper proposes Social-Temporal Group Query to find the activity time and attendees with the minimum total social distance to the initiator.  ...  For example, finding the maximum k-plexes is discussed in [11, 16, 18] , and enumeration of all maximal k-plexes is discussed in [21] .  ... 
doi:10.14778/1978665.1978671 fatcat:kok6fo7je5apnehnnmzssnahju

T-EDGE: Temporal WEighted MultiDiGraph Embedding for Ethereum Transaction Network Analysis [article]

Jiajing Wu, Dan Lin, Zibin Zheng, Qi Yuan
2019 arXiv   pre-print
Recently, graph embedding techniques have been widely used in the analysis of various networks, but most of the existing embedding methods omit the temporal and weighted information of edges which may  ...  In a TWMDG, we define the problem of Temporal Weighted Multidigraph Embedding (T-EDGE) by incorporating both temporal and weighted information of the edges, the purpose being to capture more comprehensive  ...  A summary of the dataset is listed in Table 1 .  ... 
arXiv:1905.08038v1 fatcat:luisbxm2sjd43h2o6q6sjmj4di

A classification for community discovery methods in complex networks

Michele Coscia, Fosca Giannotti, Dino Pedreschi
2011 Statistical analysis and data mining  
Since network representation can be very complex and can contain different variants in the traditional graph model, each algorithm in the literature focuses on some of these properties and establishes,  ...  Much effort has been devoted in the literature to develop methods and algorithms that can efficiently highlight this hidden structure of the network, traditionally by partitioning the graph.  ...  Michele Coscia is a recipient of the Google Europe Fellowship in Social Computing, and this research is supported in part by this Google Fellowship.  ... 
doi:10.1002/sam.10133 fatcat:vyy377nwdnc7pigfpiqfx7x3eq

An Efficient Updation Approach for Enumerating Maximal (Δ, γ)Cliques of a Temporal Network [article]

Suman Banerjee, Bithika Pal
2020 arXiv   pre-print
Enumerating such maximal cliques is an important problem in temporal network analysis, as it reveals contact pattern among the nodes of G.  ...  In this paper, we study the maximal (Δ, γ)clique enumeration problem in online setting; i.e.; the entire link set of the network is not known in advance, and the links are coming as a batch in an iterative  ...  [7] studied the reachability estimation problem in temporal graphs. Wildemann et al.  ... 
arXiv:2007.04411v1 fatcat:lcbfjwxbf5byjmiv3tv25x6aca

Core decomposition in large temporal graphs

Huanhuan Wu, James Cheng, Yi Lu, Yiping Ke, Yuzhen Huang, Da Yan, Hejun Wu
2015 2015 IEEE International Conference on Big Data (Big Data)  
be used in temporal graph analysis.  ...  In this paper, we define the problem of core decomposition in a temporal graph, propose efficient distributed algorithms to compute the cores in massive temporal graphs, and discuss how the technique can  ...  One important problem in graph analysis is to identify cohesive subgraphs, for example, (maximal) cliques, quasi-cliques, n-cliques, k-plexes, n-clans, k-cores [19] , ktrusses [20] , and other types  ... 
doi:10.1109/bigdata.2015.7363809 dblp:conf/bigdataconf/WuCLKHYW15 fatcat:ixjjqk6k65b53lasawz2devxoa

A dynamic graph visualization perspective on eye movement data

Michael Burch, Fabian Beck, Michael Raschke, Tanja Blascheck, Daniel Weiskopf
2014 Proceedings of the Symposium on Eye Tracking Research and Applications - ETRA '14  
In this paper, we propose transforming eye movement data into a dynamic graph data structure to explore the visualization problem from a new perspective.  ...  Abstract During eye tracking studies, vast amounts of spatio-temporal data in the form of eye gaze trajectories are recorded. Finding insights into these time-varying data sets is a challenging task.  ...  The set of all k defined AOIs in a stimulus is modeled as A := {A1, . . . , A k } .  ... 
doi:10.1145/2578153.2578175 dblp:conf/etra/BurchBRBW14 fatcat:rnpu5ykhn5gobbbqfdyzl5xjze
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