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Parameterized Correlation Clustering in Hypergraphs and Bipartite Graphs [article]

Nate Veldt and Anthony Wirth and David F. Gleich
2020 arXiv   pre-print
Motivated by applications in community detection and dense subgraph discovery, we consider new clustering objectives in hypergraphs and bipartite graphs.  ...  We first show that our parameterized hypergraph correlation clustering objective is related to higher-order notions of normalized cut and modularity in hypergraphs.  ...  Our objectives are based on parameterized versions of correlation clustering and we show how, in certain parameter regimes, our objectives are related to a number of these previous objectives for bipartite  ... 
arXiv:2002.09460v2 fatcat:clwha7ybzzduhkx62fx3fueefe

Hypergraph-based connectivity measures for signaling pathway topologies

Nicholas Franzese, Adam Groce, T. M. Murali, Anna Ritz, Ferhat Ay
2019 PLoS Computational Biology  
This measure, B-relaxation distance, provides a parameterized transition between hypergraph connectivity and graph connectivity.  ...  We find that Reactome is very well connected as a graph, moderately well connected as a compound graph or bipartite graph, and poorly connected as a hypergraph (which captures many-to-many relationships  ...  Acknowledgments We thank Brendan Avent for his initial work on the hypergraph algorithms library and Ozgun Babur for discussions about BioPAX and PaxTools.  ... 
doi:10.1371/journal.pcbi.1007384 pmid:31652258 pmcid:PMC6834280 fatcat:vn26pwnvozferinsmll2uivhme

Models and Methods for Sparse (Hyper)Network Science in Business, Industry, and Government

Sinan G Aksoy, Aric Hagberg, Cliff A Joslyn, Bill Kay, Emilie Purvine, Stephen J Young
2022 Notices of the American Mathematical Society  
model multi-way relations in hypergraphs, rather than only pairwise interactions in graphs; and (2) challenges posed by modeling networks with extreme sparsity.  ...  Here we introduce and explore these two themes and their challenges. We hope to generate interest from researchers in pure and applied mathematics and computer science.  ...  And while hypergraphs are bijective to bipartite graphs 2 in which one of the parts is labeled as vertices and the other as edges, naive deployment of graph methods against them will not necessarily reveal  ... 
doi:10.1090/noti2424 fatcat:hnu5w6rojraudjkchhm4k5cdrq

Characterizing the hypergraph-of-entity and the structural impact of its extensions

José Devezas, Sérgio Nunes
2020 Applied Network Science  
We also propose the calculation of a general mixed hypergraph density measure based on the corresponding bipartite mixed graph.  ...  We use a random walk based approach to estimate shortest distances and node sampling to estimate clustering coefficients.  ...  Acknowledgements We would like to thank Bruno Martins, from INESC-ID and the University of Lisbon, for his suggestion on integrating the concept of term frequency into the hypergraph-of-entity in the form  ... 
doi:10.1007/s41109-020-00320-z fatcat:kgehpp2vanb73mcyij5lq4gv4i

Networks beyond pairwise interactions: Structure and dynamics

Federico Battiston, Giulia Cencetti, Iacopo Iacopini, Vito Latora, Maxime Lucas, Alice Patania, Jean-Gabriel Young, Giovanni Petri
2020 Physics reports  
We review the measures designed to characterize the structure of these systems and the models proposed to generate synthetic structures, such as random and growing bipartite graphs, hypergraphs and simplicial  ...  Yet, from human communications to chemical reactions and ecological systems, interactions can often occur in groups of three or more nodes and cannot be described simply in terms of dyads.  ...  The presence of links among neighbors of i and j (clustering) does not affect the definition of the groups. Fig. 34 . 34 Public goods game on bipartite graphs.  ... 
doi:10.1016/j.physrep.2020.05.004 fatcat:pkugz4i5obainmcrwod6i4od7q

A simple bipartite graph projection model for clustering in networks [article]

Austin R. Benson, Paul Liu, Hao Yin
2020 arXiv   pre-print
Graph datasets are frequently constructed by a projection of a bipartite graph, where two nodes are connected in the projection if they share a common neighbor in the bipartite graph; for example, a coauthorship  ...  graph is a projection of an author-publication bipartite graph.  ...  We thank Johan Ugander for pointing us to the literature on random intersection graphs.  ... 
arXiv:2007.00761v1 fatcat:lwexjuwsbncellyq4ie36theui

Networks beyond pairwise interactions: structure and dynamics [article]

Federico Battiston, Giulia Cencetti, Iacopo Iacopini, Vito Latora, Maxime Lucas, Alice Patania, Jean-Gabriel Young, Giovanni Petri
2020 arXiv   pre-print
, bipartite graphs and hypergraphs.  ...  Yet, in face-to-face human communication, chemical reactions and ecological systems, interactions can occur in groups of three or more nodes and cannot be simply described just in terms of simple dyads  ...  The presence of links among neighbors of i and j (clustering) does not affect the definition of the groups. FIG. 35 . 35 Public goods game on bipartite graphs.  ... 
arXiv:2006.01764v1 fatcat:h4ezvequxrbyrozpjbb6lbqhj4

Generative hypergraph clustering: From blockmodels to modularity

Philip S. Chodrow, Nate Veldt, Austin R. Benson
2021 Science Advances  
We propose a probabilistic generative model of clustered hypergraphs with heterogeneous node degrees and edge sizes.  ...  Using synthetic and empirical data, we demonstrate that the specialized method is highly scalable and can detect clusters where graph-based methods fail.  ...  Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials.  ... 
doi:10.1126/sciadv.abh1303 fatcat:qb6klph6c5e3ncv7py2k6nk74u

Generative hypergraph clustering: from blockmodels to modularity [article]

Philip S. Chodrow, Nate Veldt, Austin R. Benson
2021 arXiv   pre-print
However, there are few models and algorithms for hypergraph clustering.  ...  Here, we propose a Poisson degree-corrected hypergraph stochastic blockmodel (DCHSBM), a generative model of clustered hypergraphs with heterogeneous node degrees and edge sizes.  ...  FUNDING This research was supported in part by ARO Award W911NF19-1-0057, ARO MURI, NSF Award DMS-1830274, and JP Morgan Chase & Co.  ... 
arXiv:2101.09611v4 fatcat:v2d2r7wjizf6da4jzdkwrg7ama

Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams

Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, Sofya Vorotnikova
2015 Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms  
Results include testing edge connectivity [6] and vertex connectivity [28] , constructing sparsifiers [7, 8, 33] , approximating the densest subgraph [10, 20, 43] , correlation clustering [3] , and  ...  ., c(e) is exactly 1 To see this, consider a layered graph on vertices L 1 ∪L 2 ∪L 3 ∪L 4 with edges forming a complete bipartite graph on L 1 × L 2 , a complete bipartite matching on L 2 ×L 3 , and  ... 
doi:10.1137/1.9781611974331.ch92 dblp:conf/soda/ChitnisCEHMMV16 fatcat:3jul55k3u5alboeeoughpqk6w4

Entanglement in highly symmetric multipartite quantum states [article]

Adam Burchardt, Jakub Czartowski, Karol Życzkowski
2021 arXiv   pre-print
The states constructed by this technique exhibit desired symmetry properties and form a natural resource for less-symmetric quantum informational tasks.  ...  We propose quantum circuits efficiently generating such states, which in general have smaller complexity than the circuits necessary to create fully symmetric entangled states.  ...  Following the usual notation in graph theory, let K V1V2 be a complete bipartite graph, while G = K V1...V k complete multi-partite k-hypergraph.  ... 
arXiv:2105.12721v2 fatcat:r6gpgamyc5hyzosaea7zfgvmjy

Kernelization via Sampling with Applications to Dynamic Graph Streams [article]

Rajesh Chitnis and Graham Cormode and Hossein Esfandiari and MohammadTaghi Hajiaghayi and Andrew McGregor and Morteza Monemizadeh and Sofya Vorotnikova
2015 arXiv   pre-print
In this paper we present a simple but powerful subgraph sampling primitive that is applicable in a variety of computational models including dynamic graph streams (where the input graph is defined by a  ...  The best previous algorithm used Õ(kn) space where n is the number of vertices in the graph and we prove our result is optimal up to logarithmic factors. Our algorithm has Õ(1) update time.  ...  Hitting Set and Hypergraph Matching In this section we present exact results for hitting set and hypergraph matching.  ... 
arXiv:1505.01731v1 fatcat:oh4zxrhluvcydnyynabcjidtgi

Entanglement and nonclassical properties of hypergraph states

Otfried Gühne, Martí Cuquet, Frank E S Steinhoff, Tobias Moroder, Matteo Rossi, Dagmar Bruß, Barbara Kraus, Chiara Macchiavello
2014 Journal of Physics A: Mathematical and Theoretical  
In this paper, we explore the entanglement properties and nonclassical features of hypergraph states.  ...  Finally, we consider the question whether hypergraph states and their correlations can be used to reveal contradictions with classical hidden variable theories.  ...  Appendix In Table 2 we present the 24 classes of three-uniform six-qubit hypergraph states, where all single-qubit reduced density matrices are maximally mixed.  ... 
doi:10.1088/1751-8113/47/33/335303 fatcat:odujlbj3ircj5pk7yiprocvo6m

A Unified Community Detection, Visualization and Analysis method [article]

Michel Crampes, Michel Plantié
2014 arXiv   pre-print
In the first place interest was limited to unipartite graph inputs and partitioned community outputs. Recently bipartite graphs, directed graphs and overlapping communities have been investigated.  ...  After applying our method to Human Brain Tractography Data provided by a team of neurologists, we produce clusters of white fibers in accordance with other well known clustering methods.  ...  Interestingly with this method the number of communities is parameterized by the order n. C. From unipartite to bipartite graphs.  ... 
arXiv:1301.7006v6 fatcat:njomgj6b7zgkbo7gus3aaefjie

Structural and dynamical analysis of biological networks

Cecilia Klein, Andrea Marino, Marie-France Sagot, Paulo Vieira Milreu, Matteo Brilli
2012 Briefings in Functional Genomics  
Such realizations provide snapshots of a same network in different conditions, enabling the study of condition-dependent structural properties.  ...  Their structural analysis enables to highlight nodes with special properties that have sometimes been correlated with the biological importance of a gene or a protein.  ...  These limitations ask for a full treatment of complex reactions in an MN (discussed in detail e.g. in [1, 2] ): bipartite graphs and hypergraphs help to overcome these problems at the price of a higher  ... 
doi:10.1093/bfgp/els030 pmid:22908211 fatcat:wy7c2gxj5zhg3iwrqllqagsz7m
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