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Counting Motifs with Graph Sampling
[article]
2018
arXiv
pre-print
Preserved Fulltext
This is shown to be optimal for all motifs with at most 4 vertices and cliques of all sizes. The matching minimax lower bounds are established using certain algebraic properties of subgraph counts. ...
We also address the issue of adaptation to the unknown maximum degree, and study specific problems for parent graphs with additional structures, e.g., trees or planar graphs. ...
The purpose of this paper is to develop a statistical theory for estimating motif counts in sampled graph. ...
arXiv:1802.07773v1
fatcat:2wldd24eyvajdbk772eogjqm4u
A sampling framework for counting temporal motifs
[article]
2018
arXiv
pre-print
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Pattern counting in graphs is fundamental to network science tasks, and there are many scalable methods for approximating counts of small patterns, often called motifs, in large graphs. ...
More specifically, we develop a sampling framework that sits as a layer on top of existing exact counting algorithms and enables fast and accurate memory-efficient estimates of temporal motif counts. ...
We devised a new algorithm for 2-node, 3-edge motifs that is compatible with our sampling framework. In this case, each pair of nodes in the input graph forms an independent counting problem. ...
arXiv:1810.00980v1
fatcat:xmglld2fg5atpliuvqsj2gqzje
Efficient Sampling Algorithms for Approximate Motif Counting in Temporal Graph Streams
[article]
2022
arXiv
pre-print
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The second is an improved edge-wedge sampling (EWS) algorithm that hybridizes edge sampling with wedge sampling for counting temporal motifs with 3 vertices and 3 edges. ...
In this paper, we focus on approximate temporal motif counting via random sampling. We first propose two sampling algorithms for temporal motif counting in the offline setting. ...
] , 𝑘-cliques [6, 17] , sparse motifs with low counts [47] , and butterflies in bipartite graphs [39] . ...
arXiv:2211.12101v1
fatcat:xsb37reo6reexkwq3zhcxm6ala
Multi-MotifGAN (MMGAN): Motif-targeted Graph Generation and Prediction
[article]
2019
arXiv
pre-print
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MMGAN outperforms NetGAN at creating new graphs that accurately reflect the network motif statistics of input graphs such as Citeseer, Cora and Facebook. ...
Different types of graphs contain different network motifs, an example of which are triangles that often arise in social and biological networks. ...
Raw motif counts in the generated graphs with normalization with respect to input count for better comparison. ...
arXiv:1911.05469v1
fatcat:6siywcdg7jhqxanu5ej76qohzu
Efficient Sampling Algorithms for Approximate Temporal Motif Counting (Extended Version)
[article]
2020
arXiv
pre-print
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Furthermore, we devise an improved EWS algorithm that hybridizes edge sampling with wedge sampling for counting temporal motifs with 3 vertices and 3 edges. ...
method for temporal motif counting. ...
Related Work Random Sampling for Motif Counting: In recent years, there have been great efforts to (approximately) count the number of occurrences of a motif in a large graph via random sampling. ...
arXiv:2007.14028v1
fatcat:e4rhab4rdvcbrhojws2576ok7a
Representation Learning for Frequent Subgraph Mining
[article]
2024
arXiv
pre-print
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And last, we show that SPMiner can find large up to 20 node motifs with 10-100x higher frequency than those found by current approximate methods. ...
However, finding large commonly-occurring motifs remains a challenging problem not only due to its NP-hard subroutine of subgraph counting, but also the exponential growth of the number of possible subgraphs ...
In the end, the motifs with highest visit count are selected. ...
arXiv:2402.14367v1
fatcat:ixttnqtbcnbctktzj6c4sv55ce
Path Sampling: A Fast and Provable Method for Estimating 4-Vertex Subgraph Counts
[article]
2014
arXiv
pre-print
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Indeed, even a highly tuned enumeration code takes more than a day on a graph with millions of edges. ...
The special case of triangle counting has received much attention. ...
The main challenge of motif counting is combinatorial explosion. Even in a moderately sized graph with millions of edges, the subgraph counts (even for 4-vertex patterns) is in the billions. ...
arXiv:1411.4942v1
fatcat:n6tztzp46beq7mlaugyxrgw5xu
An optimal algorithm for counting network motifs
2007
Physica A: Statistical Mechanics and its Applications
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Network motifs are small connected sub-graphs occurring at significantly higher frequencies in a given graph compared with random graphs of similar degree distribution. ...
We here present a new optimal algorithm, based on network decomposition for counting K-size network motifs with constant memory costs and a CPU cost linear with the number of counted motifs. ...
of these subgraphs are isomorphic, and count only once every isomorphic groups. (3) Comparison of the motif number with the expected number in a random graph with the same connectivity structure. ...
doi:10.1016/j.physa.2007.02.102
fatcat:rwibk7nf6jd6dlucukcjmtvgge
Which Modality should I use – Text, Motif, or Image? : Understanding Graphs with Large Language Models
[article]
2024
arXiv
pre-print
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This paper introduces a new approach to encoding a graph with diverse modalities, such as text, image, and motif, coupled with prompts to approximate a graph's global connectivity, thereby enhancing LLMs ...
The study also presents GraphTMI, a novel benchmark for evaluating LLMs in graph structure analysis, focusing on homophily, motif presence, and graph difficulty. ...
text, motif, and image) with the graph structure and sampling type shows the clear dependency of graph structure and sampling on node classification performance. ...
arXiv:2311.09862v2
fatcat:22dzomyurzdkjdm4zvfsuktz3m
Sequential Motifs in Observed Walks
[article]
2022
arXiv
pre-print
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2021 pre-print arXiv:2112.05642v1 fatcat:itkwq2jp6rejlgxjksolhmx274
We show that by mapping edges of a HON, specifically a kth-order DeBruijn graph, to sequential motifs, we can count and evaluate their importance in observed data. ...
We draw a connection between counting and analysis of sequential motifs and Higher-Order Network (HON) models. ...
For every iteration we sample w walks using each sampling method, map the walks to motifs, and accumulate the count of each motif for each method. ...
arXiv:2112.05642v2
fatcat:y2yhlnopyffo3o5ybrfe4scsqm
Quantifying Uncertainty for Temporal Motif Estimation in Graph Streams under Sampling
[article]
2022
arXiv
pre-print
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Several methods have been designed to count the occurrences of temporal motifs in graph streams, with recent work focusing on estimating the count under various sampling schemes along with concentration ...
to construct confidence intervals and conduct hypothesis testing for the temporal motif count under sampling. ...
with probability p and the local motif count around the sampled edge is observed. ...
arXiv:2202.10513v1
fatcat:dbxk3cljifeo3jtco3xka555t4
Scalable Motif Counting for Large-scale Temporal Graphs
[article]
2022
arXiv
pre-print
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In this work, we propose a scalable parallel framework for exactly counting temporal motifs in large-scale temporal graphs. ...
modern CPU to concurrently count all temporal motifs. ...
[17] propose an edge sampling algorithm for any temporal motifs and hybridize edge sampling with wedge sampling to count temporal motifs with 3 nodes and 3 edges.
III. ...
arXiv:2204.09236v1
fatcat:gy77bdmn5rg3hpbgvpabdxsgue
Hypergraph Motifs: Concepts, Algorithms, and Discoveries
[article]
2020
arXiv
pre-print
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Our algorithmic contribution is to propose MoCHy, a family of parallel algorithms for counting h-motifs' occurrences in a hypergraph. ...
We first define hypergraph motifs (h-motifs), which describe the connectivity patterns of three connected hyperedges. ...
Each instance of closed h-motifs is counted if one of the 3 hyperwedges in it is sampled, while that of open h-motifs is counted if one of the 2 hyperwedges in it is sampled. ...
arXiv:2003.01853v1
fatcat:xtol4x4zszb2bdwrmkh2cxl4ra
Hypergraph Motifs and Their Extensions Beyond Binary
[article]
2023
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2023; you can also visit the original URL.
The file type is application/pdf.
Our algorithmic contribution is to propose MoCHy, a family of parallel algorithms for counting h-motifs' occurrences in a hypergraph. ...
We first define hypergraph motifs (h-motifs), which describe the overlapping patterns of three connected hyperedges. ...
., |E ′ | do 5 v i ← sample from V with probability ∝ degree 6 e j ← sample from E with probability ∝ degree 7 add (v i , e j ) to Ẽ 8 return G = ( Ṽ , Ẽ) Transformation from Incidence Graphs to Hypergraphs ...
arXiv:2310.15668v1
fatcat:vxovujecb5cg5m6jtvgiwbrwfe
Large-scale network motif analysis using compression
[article]
2019
arXiv
pre-print
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With this new relevance test, we can search for motifs by random sampling, rather than requiring an accurate count of all instances of a motif. ...
To compute this expectation, a full or approximate count of the occurrences of a motif is normally repeated on as many as 1000 random graphs sampled from the null model; a prohibitively expensive step. ...
A.3 Sampling algorithm For the first experiment, we use the following algorithm to sample a graph with k injected motifs. ...
arXiv:1701.02026v3
fatcat:mgrse5y4ojg5bftghc7z6vsube
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