Heterogeneous Network Motifs

Rossi, Ryan A.; Ahmed, Nesreen K.; Carranza, Aldo; Arbour, David; Rao, Anup; Kim, Sung‐Chul; Koh, Eunyee

doi:10.48550/arxiv.1901.10026

Cited by 4 publications

(4 citation statements)

References 39 publications

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“…We regularize arbitrary GNNs to learn statistical correspondences between distant nodes with co-varying attribute structures. Our abstraction of roles through motifs generalizes across diverse types of networks, e.g., signed and heterogeneous motifs [38].…”

Section: Discussionmentioning

confidence: 99%

Beyond Localized Graph Neural Networks: An Attributed Motif Regularization Framework

Ashok

Wang

Krishnan

et al. 2020

2020 IEEE International Conference on Data Mining (ICDM)

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We present InfoMotif, a new semi-supervised, motifregularized, learning framework over graphs. We overcome two key limitations of message passing in popular graph neural networks (GNNs): localization (a k-layer GNN cannot utilize features outside the k-hop neighborhood of the labeled training nodes) and over-smoothed (structurally indistinguishable) representations. We propose the concept of attributed structural roles of nodes based on their occurrence in different network motifs, independent of network proximity. Two nodes share attributed structural roles if they participate in topologically similar motif instances over co-varying sets of attributes. Further, InfoMotif achieves architecture independence by regularizing the node representations of arbitrary GNNs via mutual information maximization. Our training curriculum dynamically prioritizes multiple motifs in the learning process without relying on distributional assumptions in the underlying graph or the learning task. We integrate three state-of-the-art GNNs in our framework, to show significant gains (3-10% accuracy) across six diverse, real-world datasets. We see stronger gains for nodes with sparse training labels and diverse attributes in local neighborhood structures.

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Section: Discussionmentioning

confidence: 99%

Beyond Localized Graph Neural Networks: An Attributed Motif Regularization Framework

Ashok

Wang

Krishnan

et al. 2020

2020 IEEE International Conference on Data Mining (ICDM)

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“…There is rich history of work on triangle counting in static graphs. Various algorithm for triangle and motif counting in attributed graphs have also been proposed [13,30,37,41,42,56]. Here we only focus on temporal networks and refer the reader to [2] and the tutorial [44] for a more detailed list of related work.…”

Section: Related Workmentioning

confidence: 99%

Faster and Generalized Temporal Triangle Counting, via Degeneracy Ordering

Pashanasangi

Seshadhri

2021

Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery &Amp; Data Mining

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Triangle counting is a fundamental technique in network analysis, that has received much attention in various input models. The vast majority of triangle counting algorithms are targeted to static graphs. Yet, many real-world graphs are directed and temporal, where edges come with timestamps. Temporal triangles yield much more information, since they account for both the graph topology and the timestamps.Temporal triangle counting has seen a few recent results, but there are varying definitions of temporal triangles. In all cases, temporal triangle patterns enforce constraints on the time interval between edges (in the triangle). We define a general notion ( 1,3 , 1,2 , 2,3 )-temporal triangles that allows for separate time constraints for all pairs of edges.Our main result is a new algorithm, DOTTT (Degeneracy Oriented Temporal Triangle Totaler), that exactly counts all directed variants of ( 1,3 , 1,2 , 2,3 )-temporal triangles. Using the classic idea of degeneracy ordering with careful combinatorial arguments, we can prove that DOTTT runs in ( log ) time, where is the number of (temporal) edges and is the graph degeneracy (max core number). Up to log factors, this matches the running time of the best static triangle counters. Moreover, this running time is better than existing.DOTTT has excellent practical behavior and runs twice as fast as existing state-of-the-art temporal triangle counters (and is also more general). For example, DOTTT computes all types of temporal queries in Bitcoin temporal network with half a billion edges in less than an hour on a commodity machine. CCS CONCEPTS• Theory of computation → Graph algorithms analysis; • Information systems → Data mining; Social networks; • Mathematics of computing → Graph algorithms.

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“…Rossi-Ahmed-Carranza-Arbour-Rao-Kim-Koh proposed a parallel algorithm for counting typed graphlets (subgraph patterns), which are a generalization of subgraph patterns to heterogeneous networks [47].…”

Section: Related Workmentioning

confidence: 99%

Efficiently Counting Vertex Orbits of All 5-vertex Subgraphs, by EVOKE

Pashanasangi

Seshadhri

2020

Proceedings of the 13th International Conference on Web Search and Data Mining

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Subgraph counting is a fundamental task in network analysis. Typically, algorithmic work is on total counting, where we wish to count the total frequency of a (small) pattern subgraph in a large input data set. But many applications require local counts (also called vertex orbit counts) wherein, for every vertex v of the input graph, one needs the count of the pattern subgraph involving v. This provides a rich set of vertex features that can be used in machine learning tasks, especially classification and clustering. But getting local counts is extremely challenging. Even the easier problem of getting total counts has received much research attention. Local counts require algorithms that get much finer grained information, and the sheer output size makes it difficult to design scalable algorithms.We present EVOKE, a scalable algorithm that can determine vertex orbits counts for all 5-vertex pattern subgraphs. In other words, EVOKE exactly determines, for every vertex v of the input graph and every 5-vertex subgraph H , the number of copies of H that v participates in. EVOKE can process graphs with tens of millions of edges, within an hour on a commodity machine. EVOKE is typically hundreds of times faster than previous state of the art algorithms, and gets results on datasets beyond the reach of previous methods.Theoretically, we generalize a recent "graph cutting" framework to get vertex orbit counts. This framework generate a collection of polynomial equations relating vertex orbit counts of larger subgraphs to those of smaller subgraphs. EVOKE carefully exploits the structure among these equations to rapidly count. We prove and empirically validate that EVOKE only has a small constant factor overhead over the best (total) 5-vertex subgraph counter.

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Heterogeneous Network Motifs

Cited by 4 publications

References 39 publications

Beyond Localized Graph Neural Networks: An Attributed Motif Regularization Framework

Beyond Localized Graph Neural Networks: An Attributed Motif Regularization Framework

Faster and Generalized Temporal Triangle Counting, via Degeneracy Ordering

Efficiently Counting Vertex Orbits of All 5-vertex Subgraphs, by EVOKE

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