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Denser than the densest subgraph

Charalampos Tsourakakis, Francesco Bonchi, Aristides Gionis, Francesco Gullo, Maria Tsiarli
2013 Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '13  
Surprisingly enough, however, densest subgraphs are typically large graphs, with small edge density and large diameter.  ...  A very popular among such functions is the average degree, whose maximization leads to the well-known densest-subgraph notion.  ...  Still, the triangle density of the optimal quasi-cliques outputted by both GreedyOQC and Local-SearchOQC is one order of magnitude larger than the triangle density of densest subgraphs on 11 out of 15  ... 
doi:10.1145/2487575.2487645 dblp:conf/kdd/TsourakakisBGGT13 fatcat:hqpalkyi5fbjdjakjkvonootyu

K-clique-graphs for Dense Subgraph Discovery [article]

G. Nikolentzos, P. Meladianos, Y. Stavrakas, M. Vazirgiannis
2018 arXiv   pre-print
In this paper we focus on the triangle-graph densest subgraph problem obtained for k=3.  ...  In this paper, we introduce the k-clique-graph densest subgraph problem, k >= 3, a novel formulation for the discovery of dense subgraphs.  ...  The proposed triangle-graph densest subgraph (TGDS) problem seems to be very related to the triangle densest subgraph (TDS) problem introduced by Tsourakakis in [31] .  ... 
arXiv:1610.06008v3 fatcat:xgnb4al7szgfresyk2aa2z2rjm

Parallel Algorithms for Densest Subgraph Discovery Using Shared Memory Model [article]

B.D.M. De Zoysa, Y.A.M.M.A. Ali, M.D.I. Maduranga, Indika Perera, Saliya Ekanayake, Anil Vullikanti
2021 arXiv   pre-print
Furthermore, efforts were also steered towards devising a novel algorithm for the problem of densest subgraph discovery.  ...  This paper presents an improved implementation of a widely used densest subgraph discovery algorithm and a novel parallel algorithm which produces better results than a 2-approximation.  ...  Top-k local triangle-densest subgraph discovery is based on the 3-clique and has been studied in [41] . Fang et al.  ... 
arXiv:2103.00154v1 fatcat:ghhhsir4jrajvoczhgyqht2dn4

Where Graph Topology Matters: The Robust Subgraph Problem [chapter]

Hau Chan, Shuchu Han, Leman Akoglu
2015 Proceedings of the 2015 SIAM International Conference on Data Mining  
In this paper, we turn attention to local robustness and pose a novel problem in the lines of subgraph mining: given a large graph, how can we find its most robust local subgraph (RLS)?  ...  Experiments on synthetic and real-world graphs demonstrate that we find subgraphs with larger robustness than the densest subgraphs [9, 39] even at lower densities, suggesting that the existing approaches  ...  In this paper, we turn attention to local robustness and pose a novel subgraph mining problem: given a large graph, how can we find its most robust local subgraph of a given size?  ... 
doi:10.1137/1.9781611974010.2 dblp:conf/sdm/ChanHA15 fatcat:levvxdxfgveahhcf2ibmshdzpa

Dense Packing on Uniform Lattices

Kari Eloranta
2007 Journal of statistical physics  
Our particular aim in choosing these graphs is to obtain insight to the geometry of the densest packings in a uniform discrete set-up.  ...  These phenomena are related to the exponential size of the set of densest packings and more specifically whether these packings are maximally symmetric, simple laminated or essentially random packings.  ...  The lack of a local move implies long range order whereas the existence of a local move enables one to join densest finite patches into a densest global configuration.  ... 
doi:10.1007/s10955-007-9448-0 fatcat:f44mzeiqwnbkfoqfvzojtol7dm

Efficient algorithms for densest subgraph discovery

Yixiang Fang, Kaiqiang Yu, Reynold Cheng, Laks V. S. Lakshmanan, Xuemin Lin
2019 Proceedings of the VLDB Endowment  
Densest subgraph discovery (DSD) is a fundamental problem in graph mining.  ...  Our main observation is that the densest subgraph can be accurately found through a k-core (a kind of dense subgraph of G), with theoretical guarantees.  ...  Recently, a variant based on the 3-clique, called top-k local triangle-densest subgraphs discovery, has been investigated [57] .  ... 
doi:10.14778/3342263.3342645 fatcat:egfsgtjzsnbsbkazs26vath2f4

Density-friendly Graph Decomposition

Nikolaj Tatti, Aristides Gionis
2015 Proceedings of the 24th International Conference on World Wide Web - WWW '15  
Simply put, the most central k-core is not necessarily the densest subgraph. This inconsistency between k-cores and graph density provides the basis of our study.  ...  We start by defining what it means for a subgraph to be locally-dense, and we show that our definition entails a nested chain decomposition of the graph, similar to the one given by k-cores, but in this  ...  Recently, Tsourakakis proposed to measure density by counting triangles, instead of counting edges [26] .  ... 
doi:10.1145/2736277.2741119 dblp:conf/www/TattiG15 fatcat:izsimms4ojaslkbbpjnizdy6j4

Where Graph Topology Matters: The Robust Subgraph Problem [article]

Hau Chan and Shuchu Han and Leman Akoglu
2015 arXiv   pre-print
In this paper, we turn attention to local robustness and pose a novel problem in the lines of subgraph mining: given a large graph, how can we find its most robust local subgraph (RLS)?  ...  Experiments on synthetic and real-world graphs demonstrate that we find subgraphs with larger robustness than the densest subgraphs even at lower densities, suggesting that the existing approaches are  ...  Experiments on synthetic and real graphs showed that our subgraphs are of higher robustness than densest subgraphs even at lower densities, which illustrates the novelty of our problem setting.  ... 
arXiv:1501.01939v1 fatcat:3bcb5blu2nhxnedxzgqlt4tekq

Peeling Bipartite Networks for Dense Subgraph Discovery [article]

A. Erdem Sariyuce, Ali Pinar
2017 arXiv   pre-print
We study the dense subgraph discovery problem on bipartite graphs.  ...  However, most dense subgraph discovery algorithms are designed for classic, unipartite graphs.  ...  Furthermore, W results in pre y competitive subgraphs with respect to the bu er y densest subgraph.  ... 
arXiv:1611.02756v3 fatcat:zqowwtntu5hnjad2aeonx5qxpq

Connected-Dense-Connected Subgraphs in Triple Networks [article]

Dhara Shah, Yubao Wu, Sushil Prasad, Danial Aghajarian
2020 arXiv   pre-print
We also study different variations of the CDC subgraphs.  ...  We show that finding CDC subgraphs is NP-hard and develop novel heuristics to obtain feasible solutions, the fastest of which is O(nlogn+m) with n nodes and m edges.  ...  NYC Taxi data Figure 3 illustrates CDC and OCD subgraphs with pick-up and drop-off points as triangles and circles respectively.  ... 
arXiv:2011.09408v1 fatcat:h4ip2za2kvb4fmk2c54robzdia

Mining Large Quasi-cliques with Quality Guarantees from Vertex Neighborhoods [article]

Aritra Konar, Nicholas D. Sidiropoulos
2020 arXiv   pre-print
The implementation of such a method requires counting the triangles in a graph, which is a well-studied problem in graph mining.  ...  For graphs with small clustering coefficients, we demonstrate that small vertex neighborhoods can be refined using a local-search method to "grow" larger cliques and near-cliques.  ...  NB -neighborhood, NB+LS -local search with neighborhood seeds, GRDY -greedyOQC, TDS -flow based algorithm of [26] for computing the triangle densest subgraph.  ... 
arXiv:2008.07996v1 fatcat:4fwzaqqwfrh6rczgsnsbb6tgh4

Large Scale Density-friendly Graph Decomposition via Convex Programming

Maximilien Danisch, T.-H. Hubert Chan, Mauro Sozio
2017 Proceedings of the 26th International Conference on World Wide Web - WWW '17  
Our algorithm is even more efficient for the more specialized problem of computing a densest subgraph.  ...  In our work, we devise an efficient algorithm which is able to compute exact locally-dense decompositions in real-world graphs containing up to billions of edges.  ...  A subgraph H of G is a densest subgraph if and only if H has maximum density among all subgraphs of G. Observe that a densest subgraph is a subgraph induced by some subset of nodes.  ... 
doi:10.1145/3038912.3052619 dblp:conf/www/DanischCS17 fatcat:wnbxddby3nbkfarre5bxrujw3e

OCSM : Finding Overlapping Cohesive Subgraphs with Minimum Degree [article]

Junghoon Kim, Sungsu Lim, Jungeun Kim
2022 arXiv   pre-print
Cohesive subgraph discovery in a network is one of the fundamental problems and investigated for several decades.  ...  To the best of our knowledge, this is the first work to identify overlapping cohesive subgraphs with minimum degree by incorporating the graph density.  ...  SEA algorithm uses expansion approaches by combining Goldberg's densest subgraph algorithm [29] and a local expansion approach [11] with a reweightening scheme.  ... 
arXiv:2202.03255v2 fatcat:c2xunrbf6rcv7pxeo2h5mspyny

The Wedge Picking Model: A Theoretical Analysis of Graph Evolution Caused by Triadic Closure and Algorithmic Implications

2021 Journal of Strategic Innovation and Sustainability  
We demonstrate the applicability of our method by applying it to the densest subgraph and tri-densest subgraph discovery problem.  ...  We present a similar algorithm for finding tri-densest subgraph (a subgraph with maximum density of triangles) in the Section 4.2.  ...  Finding Tri-Densest Subgraph Algorithms for densest subgraph may output subgraphs with small clustering coefficient and large diameter.  ... 
doi:10.33423/jsis.v16i3.4442 fatcat:vvgbqy5olbhrlkr3dakoye2yfe

Scalable Large Near-Clique Detection in Large-Scale Networks via Sampling

Michael Mitzenmacher, Jakub Pachocki, Richard Peng, Charalampos Tsourakakis, Shen Chen Xu
2015 Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '15  
When k = 2, the problem becomes the well-known densest subgraph problem (DSP) [22, 31, 33, 39] .  ...  In this paper we focus on a family of poly-time solvable formulations, known as the k-clique densest subgraph problem (k-Clique-DSP) [57] .  ...  In these synthetic graphs we observe that while ρ * 2 grows, when examining ρ * 3 we find a triangle densest subgraph contains on average about 2 triangles per vertex.  ... 
doi:10.1145/2783258.2783385 dblp:conf/kdd/MitzenmacherPPT15 fatcat:gmn7sydbezhx3etolrwjameehu
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