Filtering Methods for Subgraph Matching on Multiplex Networks

Moorman, Jacob D.; Chen, Qinyi; Tu, Thomas K.; Boyd, Zachary M.; Bertozzi, Andrea L.

doi:10.1109/bigdata.2018.8622566

Cited by 27 publications

(9 citation statements)

References 12 publications

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“…While hard seeds are costly and often unavailable in practice, there are many scalable procedures in the literature for automatically generating soft seed matches. Here, we use as a soft-seeding the output of [29], a filtering approach for finding all subgraphs of the background network homomorphic to the template.…”

Section: Methodsmentioning

confidence: 99%

“…For each node in the template, the output of [29] produces a multiset of candidate matches in the background, where each candidate match corresponds to a template copy contained in the background as a subgraph (not necessarily as an induced subgraph). We convert the candidate matches into probabilities by simply converting the multiset to a count vector and normalizing the count vector to sum to 1.…”

Section: Methodsmentioning

confidence: 99%

“…These errors may be due to missing edges/vertices in the template or background, and arise in a variety of real data settings [34]. The subgraph isomorphism problem-given a template A, determine if an isomorphic copy of A exists in a larger network B and find the isomorphic copy (or copies) if it exists-has been the subject of voluminous research in the monoplex (i.e., single layer) setting, with approaches based on efficient tree search [38], color coding [3,2], graph homomorphisms [18], rule-based/filter-based matchings [10,29], among others; for a survey of the literature circa 2012, see [24]. In contrast, the problem of multilayer homomorphic/isomorphic subgraph detection is still in its relative infancy, with comparatively fewer existing methods in the literature; see, for example, [41,37,29].…”

Section: Introductionmentioning

confidence: 99%

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Multiplex graph matching matched filters

Pantazis

Sussman

Park

et al. 2019

2019 IEEE International Conference on Big Data (Big Data)

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We consider the problem of detecting a noisy induced multiplex template network in a larger multiplex background network. Our approach, which extends the framework of [36] to the multiplex setting, leverages a multiplex analogue of the classical graph matching problem to use the template as a matched filter for efficiently searching the background for candidate template matches. The effectiveness of our approach is demonstrated both theoretically and empirically, with particular attention paid to the potential benefits of considering multiple channels.for a definition of multiplex isomorphism), accounting for the reality that relatively large, complex subgraph templates may only errorfully occur in the larger background network. These errors may be due to missing edges/vertices in the template or background, and arise in a variety of real data settings [34]. The subgraph isomorphism problem-given a template A, determine if an isomorphic copy of A exists in a larger network B and find the isomorphic copy (or copies) if it exists-has been the subject of voluminous research in the monoplex (i.e., single layer) setting, with approaches based on efficient tree search [38], color coding [3, 2], graph homomorphisms [18], rule-based/filter-based matchings [10,29], among others; for a survey of the literature circa 2012, see [24]. In contrast, the problem of multilayer homomorphic/isomorphic subgraph detection is still in its relative infancy, with comparatively fewer existing methods in the literature; see, for example, [41,37,29]. Notation: The following notation will be used throughout. For an integer n > 0, we will define [n] := {1, 2, . . . , n}, J n to be the n × n hollow matrix with all off-diagonal entries identically set to 1, 0 n to be the n × n matrix with all entries identically set to 0,

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multiplex graph matching matched filters

Pantazis

Sussman

Park

et al. 2019

2019 IEEE International Conference on Big Data (Big Data)

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“…The leading and most common type of multi-layer network is multiplex networks, most suitable for dealing with empirical data. [27], [28], [29], [30]. Multiplex Networks illustrate the advantages of isomorphism.…”

Section: Multiplex Networkmentioning

confidence: 99%

Microscopic Structural Analysis of Complex Networks: An Empirical Study Using Motifs

2022

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Complex Networks can depict a clear image of real-world systems. A real-world scenario can be represented a graph with interconnected layers -called a multi-layer network. Finding motifs can give an idea of the topology of complex systems and helps to understand the dynamics in the graphs. Looking at motifs as atoms of the network is helpful to analyze the relationship between nodes, and between layers. In this work, we suggest a sub-graph enumeration approach to find and count the motifs in multi-layer network. The proposed work has many application in graph mining, particularly to structure and dynamics of complex networks.INDEX TERMS complex networks , isomorphism , graph enumeration , motifs.

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“…Additionally, based on filter methods from Moorman, Chen, Tu, Boyd, and Bertozzi (2018), the authors of that paper also provided a list of candidate matches for each template node, where the true correspondence is guaranteed to be among the candidates. The number of candidates ranges from 3 to 1059 at most, with an average of 241 candidates for each template vertex.…”

Section: Example: Britain Transportation Networkmentioning

confidence: 99%

iGraphMatch: an R Package for the Analysis of Graph Matching

Qiao¹,

Sussman²

2021

Preprint

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iGraphMatch is an R package for finding corresponding vertices between two graphs, also known as graph matching. The package implements three categories of prevalent graph matching algorithms including relaxation-based, percolation-based, and spectralbased, which are applicable to matching graphs under general settings: weighted directed graphs of different order and graphs of multiple layers. We provide versatile options to incorporate prior information in the form of seeds with or without noise and similarity scores. In addition, iGraphMatch provides functions to summarize the graph matching results in terms of several evaluation measures and visualize the matching performance. Finally, the package enables users to sample correlated random graph pairs from classic random graph models to generate data for simulations. This paper illustrates the practical applications of the package to the analysis of graph matching by detailed examples using real data from communication, neuron, and transportation networks.

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Filtering Methods for Subgraph Matching on Multiplex Networks

Cited by 27 publications

References 12 publications

Multiplex graph matching matched filters

Multiplex graph matching matched filters

Microscopic Structural Analysis of Complex Networks: An Empirical Study Using Motifs

iGraphMatch: an R Package for the Analysis of Graph Matching

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