Applications of Structural Equivalence to Subgraph Isomorphism on Multichannel Multigraphs

Nguyen, Thien Bao; Yang, Dongyun; Ge, Yurun; Li, Hao; Bertozzi, Andrea L.

doi:10.1109/bigdata47090.2019.9006538

Cited by 8 publications

(4 citation statements)

References 18 publications

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“…This paper takes inspiration for the general subgraph tree search structure from [51] and shares many of the same test cases on multichannel networks. In our previous work [42], we introduced a simpler notion of candidate equivalence and candidate structure, and tested it on a small selection of multichannel networks. From these prior works, we observed the high combinatorial complexity of the solution spaces necessitating an approach which can exploit symmetry to compress the solution space and accelerate search.…”

Section: B Paper Outlinementioning

confidence: 99%

Structural Equivalence in Subgraph Matching

Yang¹,

Ge²,

Nguyen³

et al. 2023

Preprint

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Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the efficiency of subgraph isomorphism algorithms. We introduce rigorous definitions of structural equivalence and establish conditions for when it can be safely used to generate more solutions. We illustrate how to adapt standard search routines to utilize these symmetries to accelerate search and compactly describe the solution space. We then adapt a state-of-the-art solver and perform a comprehensive series of tests to demonstrate these methods' efficacy on a standard benchmark set. We extend these methods to multiplex graphs and present results on large multiplex networks drawn from transportation systems, social media, adversarial attacks, and knowledge graphs.

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Section: B Paper Outlinementioning

confidence: 99%

Structural Equivalence in Subgraph Matching

Yang¹,

Ge²,

Nguyen³

et al. 2023

Preprint

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“…Templates with a large amount of symmetry, as in IvySys Version 11 (Section 4.4.5), can lead to a huge number of subgraph isomorphisms (SIs) that differ very little. However, these SIs can often be summarized using the concept of structural equivalence to group similar SIs together [46]. In the future, we aim to incorporate the concept of equivalence into our algorithm to improve performance and provide additional insight into the structure of the solution space.…”

Section: Future Workmentioning

confidence: 99%

Subgraph Matching on Multiplex Networks

Moorman

Chen

et al. 2021

IEEE Trans. Netw. Sci. Eng.

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An active area of research in computational science is the design of algorithms for solving the subgraph matching problem to find copies of a given template graph in a larger world graph. Prior works have largely addressed single-channel networks using a variety of approaches. We present a suite of filtering methods for subgraph isomorphisms for multiplex networks (with different types of edges between nodes and more than one edge within each channel type). We aim to understand the entire solution space rather than focusing on finding one isomorphism. Results are shown on several classes of datasets: (a) Sudoku puzzles mapped to the subgraph isomorphism problem, (b) Erd ős-R ényi multigraphs, (c) real-world datasets from Twitter and transportation networks, (d) synthetic data created for the DARPA MAA program.

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“…We will use the standard notation, A(Γ), to denote the adjacency matrix of a graph Γ. The following theorem, regarding edges within equivalence classes, can be found in [9].…”

Section: The Connection Between Structural Equivalence and Rank(i + A...mentioning

confidence: 99%

“…The complete skeleton of a graph Γ, as defined above, is very closely related with the compression graph of Γ. Compression graphs have been considered previously (see [9]), but we will approach this problem in a slightly different way. Figure 3 provides an example to help visualize what complete skeletons of graphs may look like.…”

Section: Theorem 41 If a Class Of Structurally Equivalent Vertices Ha...mentioning

confidence: 99%

Structural Equivalence in Graphs and Complete Skeletons

Higgins¹

2020

Preprint

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Two vertices u and v of a graph Γ are strucuturally equivalent if and only if the transposition (u v) is in Aut(Γ), the automorphism group of Γ. Some properties of structural equivalence and the group of vertex permutations generated by the transpositions in Aut(Γ) are discussed, along with the prime graphs of these groups. The notion of structural equivalence is used to develop a way of reconfiguring graphs into what are called their complete skeletons, which is closely related to compression graphs. Finally, the complete skeleton of a graph Γ, denoted Ω(Γ), is used to find a formula for rank(I + A(Γ)), which is helpful for determining the multiplicity of the -1 eigenvalue of Γ.

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Applications of Structural Equivalence to Subgraph Isomorphism on Multichannel Multigraphs

Cited by 8 publications

References 18 publications

Structural Equivalence in Subgraph Matching

Structural Equivalence in Subgraph Matching

Subgraph Matching on Multiplex Networks

Structural Equivalence in Graphs and Complete Skeletons

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