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Graph Clustering using Effective Resistance [article]

Vedat Levi Alev, Nima Anari, Lap Chi Lau, Shayan Oveis Gharan
2017 arXiv   pre-print
δ^-1 fraction of the weights are between clusters, i.e. w(E - ∪_i = 1^h E(V_i)) ≲w(E)/δ; ∙ the effective resistance diameter of each of the induced subgraphs G[V_i] is at most δ^3 times the average weighted  ...  This implies that very mildly expanding graphs have constant effective resistance diameter. We believe that this connection could be of independent interest in algorithm design.  ...  Acknowledgements We would like to thank Hong Zhou for helpful discussions and anonymous referees for their useful suggestions.  ... 
arXiv:1711.06530v1 fatcat:cqe3mq5dyjf2tm7eugmyepuxqi

Multilayer Clustered Graph Learning [article]

Mireille El Gheche, Pascal Frossard
2020 arXiv   pre-print
The regularization is based on a measure of graph sparsification called "effective resistance", coupled with a penalization of the first few eigenvalues of the representative graph Laplacian matrix to  ...  or clusters that are crucial in the analysis of graph data.  ...  In this paper, we use the effective resistance to measure the sparsification of a graph.  ... 
arXiv:2010.15456v1 fatcat:n3waelti2nbb5k7hwlanucrag4

Graph measures and network robustness [article]

W. Ellens, R.E. Kooij
2013 arXiv   pre-print
The measures discussed in this paper are based on the concepts of connectivity (including reliability polynomials), distance, betweenness and clustering.  ...  Some other measures are notions from spectral graph theory, more precisely, they are functions of the Laplacian eigenvalues.  ...  The effective graph resistance is the sum of the effective resistances over all pairs of vertices.  ... 
arXiv:1311.5064v1 fatcat:d23gurhxszb2hbvawcye5orhky

On the definiteness of the weighted Laplacian and its connection to effective resistance

Daniel Zelazo, Mathias Burger
2014 53rd IEEE Conference on Decision and Control  
For a graph with a single negative weight edge, we show that the weighted Laplacian becomes indefinite if the magnitude of the negative weight is less than the inverse of the effective resistance between  ...  This work explores the definiteness of the weighted graph Laplacian matrix with negative edge weights.  ...  The graph Laplacian has also proved useful in the study of random walks and Markov chains, graph partitioning, spectral clustering, and more [4] - [6] .  ... 
doi:10.1109/cdc.2014.7039834 dblp:conf/cdc/ZelazoB14 fatcat:xi3ac7ir3jh5bc6akuhibc55xq

Network-theoretic approach to sparsified discrete vortex dynamics

Aditya G. Nair, Kunihiko Taira
2015 Journal of Fluid Mechanics  
The interaction of the vortices is represented with a graph, which allows the use of network-theoretic approaches to identify key vortex-to-vortex interactions.  ...  Identification of vortex structures based on graph sparsification and sparse vortex dynamics is illustrated through an example of point-vortex clusters interacting amongst themselves.  ...  Douglas Smith) and the US Army Research Office (Grant W911NF-14-1-0386, Program Manager: Dr. Samuel Stanton).  ... 
doi:10.1017/jfm.2015.97 fatcat:jovcuzxr4jbhbeq6y4opujqiea

Predictability of Network Robustness from Spectral Measures

Kazuyuki Yamashita, Yuichi Yasuda, Ryo Nakamura, Hiroyuki Ohsaki
2020 Journal of Information Processing  
Our finding includes that, among five types of spectral measures, the effective resistance is most suitable for predicting the largest cluster component size under low node removal ratio, and that the  ...  predictability of the effective resistance is stable among different types of networks.  ...  Effective resistance implies the robustness of a graph [5] .  ... 
doi:10.2197/ipsjjip.28.551 fatcat:hrpijx44hve7pifkf6p7xuun2a

Network criticality in vehicular networks

Ali Tizghadam, Weiwei Li, Alberto Leon-Garcia
2012 Performance Evaluation Review  
Network criticality (resistance distance) is a graph-theoretic metric that quantifies network robustness, and that was originally designed to capture the effect of environmental changes in core communication  ...  importance in a graph.This results provides a basis for designing robust clustering algorithms for vehicular networks.  ...  Network criticalityτ is then the unweighted average of the effective resistances in the equivalent resistive network.  ... 
doi:10.1145/2425248.2425278 fatcat:uab7q2qwnjbhhn4zenbuyj7lwa

Multilayer Graph Clustering with Optimized Node Embedding [article]

Mireille El Gheche, Pascal Frossard
2021 arXiv   pre-print
The regularization pushes for a sparse and community-aware graph, and it is based on a measure of graph sparsification called "effective resistance", coupled with a penalization of the first few eigenvalues  ...  We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities.  ...  Now, let us define the pseudoinverse of L as 1 The set of valid combinatorial graph Laplacian matrices defined as ) and the total effective resistance amounts to [23] L † = (L + 11 /N ) −1 − 11  ... 
arXiv:2103.16534v1 fatcat:3m3xqojolfgs5obzg64xximwni

Fast Community Detection with Graph Sparsification [chapter]

Jesse Laeuchli
2020 Lecture Notes in Computer Science  
A popular approach is to use spectral methods where the Graph Laplacian L of the given graph is created, and the Fiedler vector of the graph is found.  ...  This vector is then used to cluster nodes in the same community. While a robust method, it can be expensive to compute the Fiedler vector exactly.  ...  Conclusion and Future Work In this paper we explored the use of sparsifying by effective resistance and scaled effective resistances in order to recover sparsify SBMs, as well as effective stopping criteria  ... 
doi:10.1007/978-3-030-47426-3_23 fatcat:me7yxzacw5c3pa4xeis4sxfw3i

Spectral Sparsification of Simplicial Complexes for Clustering and Label Propagation [article]

Braxton Osting, Sourabh Palande, Bei Wang
2019 arXiv   pre-print
As a generalization of the use of graphs to describe pairwise interactions, simplicial complexes can be used to model higher-order interactions between three or more objects in complex systems.  ...  In particular, we introduce a generalized effective resistance for simplices, provide an algorithm for sparsifying simplicial complexes at a fixed dimension, and give a specific version of the generalized  ...  For i = 1, the generalized effective resistance reduces to the effective resistance on the graph [30] .  ... 
arXiv:1708.08436v3 fatcat:zspxcutlorhjbkkysska7yh43u

Discovery of Influenza A Virus Sequence Pairs and Their Combinations for Simultaneous Heterosubtypic Targeting that Hedge against Antiviral Resistance

Keng Boon Wee, Raphael Tze Chuen Lee, Jing Lin, Zacharias Aloysius Dwi Pramono, Sebastian Maurer-Stroh, Sergei L. Kosakovsky Pond
2016 PLoS Computational Biology  
The identity of target sequence pairs for heterosubtypic targeting and their combinations for hedging antiviral resistance are useful toolkits to construct target graphs for different therapeutic objectives  ...  target sequence or a graph is considered resistant when it cannot achieve 100% heterosubtypic coverage.  ...  HF of all possible 2-, 3-and 4-vertices graphs are shown. Complete graphs are demarcated by a border. (B) Maximum HF of effective Duals clusters.  ... 
doi:10.1371/journal.pcbi.1004663 pmid:26771381 pmcid:PMC4714944 fatcat:fkxedrairjfutlivqsevvulz7i

On the Interplay Between Strong Regularity and Graph Densification [chapter]

Marco Fiorucci, Alessandro Torcinovich, Manuel Curado, Francisco Escolano, Marcello Pelillo
2017 Lecture Notes in Computer Science  
Among the many topological measures we test the effective resistance (or equivalently the scaled commute time), one of the most important metrics between the vertices in the graph, which has been very  ...  In particular, we use the regularity lemma to reduce an input graph and we then exploit the key lemma to obtain an expanded version which preserves some topological properties of the original graph.  ...  We use the effective resistance to assess to what extent G ′ retains the metric information that can be inferred from G.  ... 
doi:10.1007/978-3-319-58961-9_15 fatcat:peblnawydzhmlbrw6w477lbkui

Faster Spectral Sparsification in Dynamic Streams [article]

Michael Kapralov and Aida Mousavifar and Cameron Musco and Christopher Musco and Navid Nouri
2019 arXiv   pre-print
ball-carving on the input graph using (an approximation to) its effective resistance metric.  ...  Our main technical contribution is a novel method for 'bucketing' vertices of the input graph into clusters that allows fast recovery of edges of high effective resistance: the buckets are formed by performing  ...  We start with a technical lemma: on any graph with low maximum effective resistance (eventually, our low effective resistance diameter clusters) a set of vertex demands can be satisfied with a low energy  ... 
arXiv:1903.12165v1 fatcat:yxhpopn5ifbzvcedq6o24trzoe

Inter-cluster Transmission Control Using Graph Modal Barriers [article]

Leiming Zhang, Brian M. Sadler, Rick S. Blum, Subhrajit Bhattacharya
2020 arXiv   pre-print
In this paper we consider the problem of transmission across a graph and how to effectively control/restrict it with limited resources.  ...  We also develop approximations that allow low complexity distributed computation of the barrier weights using only neighborhood communication on the graph.  ...  effective for graphs that have sparsely connected clusters.  ... 
arXiv:2010.04790v1 fatcat:uj2rulbv5rav7ie3zxnmko2bya

On the Interplay between Strong Regularity and Graph Densification [article]

Marco Fiorucci, Alessandro Torcinovich, Manuel Curado, Francisco Escolano, Marcello Pelillo
2017 arXiv   pre-print
Our experiments show that this method is quite robust to the natural sparsification of proximity graphs. In addition, this robustness can be enforced by graph densification.  ...  In this paper we analyze the practical implications of Szemer\'edi's regularity lemma in the preservation of metric information contained in large graphs.  ...  We use the effective resistance to assess to what extent G ′ retains the metric information that can be inferred from G.  ... 
arXiv:1703.07107v1 fatcat:sftpy6ckpffchgmt55crsuetge
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