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Distributed Estimation of Graph 4-Profiles
2016
Proceedings of the 25th International Conference on World Wide Web - WWW '16
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We also study the more complicated problem of estimating the local 4-profiles centered at each vertex of the graph. ...
We present a novel distributed algorithm for counting all four-node induced subgraphs in a big graph. ...
At each vertex v, each combinatorial equation relates a linear combination of the local 4-subgraph counts to the count of a pair of 3-subgraphs sharing an edge va. ...
doi:10.1145/2872427.2883082
dblp:conf/www/ElenbergSBD16
fatcat:jjthhjhbajebxghx4fqi3lwauq
Estimation of Graphlet Counts in Massive Networks
2018
IEEE Transactions on Neural Networks and Learning Systems
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than 1% relative error; (d) scalable and space efficient for massive networks with billions of edges; and (e) effective for a variety of real-world settings as well as estimating global and local graphlet ...
Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. ...
For instance, instead of using PGD [13] to count graphlets (as done in this paper), one can always use the fastest state-of-the-art subgraph counting algorithm. ...
doi:10.1109/tnnls.2018.2826529
pmid:29994543
fatcat:ckfw6llcijdmrivjz7h2omaici
Beyond Triangles: A Distributed Framework for Estimating 3-profiles of Large Graphs
[article]
2015
arXiv
pre-print
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Further, we study the problem of estimating local and ego 3-profiles, two graph quantities that characterize the local neighborhood of each vertex of a graph. ...
We study the problem of approximating the 3-profile of a large graph. 3-profiles are generalizations of triangle counts that specify the number of times a small graph appears as an induced subgraph of ...
[1] develops subgraph estimators for clustering coefficient, triangle count, and wedge count in a streaming sub-sampled graph. ...
arXiv:1506.06671v1
fatcat:hr4pbfp6ezffjiwz7sfkz6xmzq
Beyond Triangles
2015
Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '15
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Further, we study the problem of estimating local and ego 3-profiles, two graph quantities that characterize the local neighborhood of each vertex of a graph. ...
We study the problem of approximating the 3-profile of a large graph. 3-profiles are generalizations of triangle counts that specify the number of times a small graph appears as an induced subgraph of ...
[1] develops subgraph estimators for clustering coefficient, triangle count, and wedge count in a streaming sub-sampled graph. ...
doi:10.1145/2783258.2783413
dblp:conf/kdd/ElenbergSBD15
fatcat:ccyhwydbebe5jbifh3juuo5fjq
Systematic identification of statistically significant network measures
2005
Physical Review E
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Key improvements over existing approaches include discovery of "motif-hubs" (multiple overlapping significant subgraphs), computational efficiency relative to subgraph census, and flexibility (the method ...
., a set of measures on graphs) for performing statistical analyses of networks. ...
We thank the organizers of the LANL/CNLS conference on "Networks: Structure, Dynamics, and Function." C.W. was supported in part by NSF Grant No. ECS-0332479, NSF Grant No. ...
doi:10.1103/physreve.71.016110
pmid:15697661
fatcat:mscmmn7gsbfqddr6b5lsncljn4
Distributed Estimation of Graph 4-Profiles
[article]
2016
arXiv
pre-print
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We also study the more complicated problem of estimating the local 4-profiles centered at each vertex of the graph. ...
We present a novel distributed algorithm for counting all four-node induced subgraphs in a big graph. ...
At each vertex v, each combinatorial equation relates a linear combination of the local 4-subgraph counts to the count of a pair of 3-subgraphs sharing an edge va. ...
arXiv:1510.02215v2
fatcat:o7nklg5wxjerlhanopepn4vr3u
Technology mapping algorithms for hybrid fpgas containing lookup tables and plas
2003
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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A breadth-first search-based subgraph extraction and evaluation heuristic is integrated with product term (Pterm) count, area, and delay estimators to guide the technology mapping process. ...
Present commercial tools, which target these hybrid devices, require hand partitioning of user designs to isolate logic for each type of logic resource. ...
Since Pterm count must be evaluated for each subgraph, the Pterm count estimator runtime impacts the usability of the estimator. ...
doi:10.1109/tcad.2003.810743
fatcat:vp4jmm4pzresfj7gtmvysfshj4
Area-Optimized Technology Mapping for Hybrid FPGAs
[chapter]
2000
Lecture Notes in Computer Science
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It is shown that fast estimation of post-minimization product term counts plays an especially important role in the mapping of designs to PLAs. ...
The subgraphs are subsequently mapped to assigned target resources. ...
product term estimation was outlined that can estimate the post-minimization product term count of a subgraph prior to the application of Espresso. ...
doi:10.1007/3-540-44614-1_21
fatcat:pyn3dupgqrbdhfzrmir2756ey4
Clique Counting in MapReduce
2015
ACM Journal of Experimental Algorithmics
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2014 pre-print arXiv:1403.0734v1 fatcat:g3ruchc5f5b3fjkqqrbxkqm664Other Versions
We tackle the problem of counting the number of k-cliques in large-scale graphs, for any constant k > 3. ...
Clique counting is essential in a variety of applications, among which social network analysis. ...
The local space and the local running time of mappers and reducers are O(m) and O(m (k−1)/2 ), respectively. • We propose sampling-based estimators that can reduce dramatically the running time and local ...
doi:10.1145/2794080
fatcat:hjibwlgr5za75dbcz3hymkavsy
Page 2859 of Mathematical Reviews Vol. , Issue 90E
[page]
1990
Mathematical Reviews
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This paper provides central limit theorems for some subgraph counts such as the count of all subgraphs in G,,, of order v and of size s, the count of subgraphs isomorphic to H, the count of induced subgraphs ...
isomorphic to H, the count of subgraphs with r edges, and so on. ...
Counting Arbitrary Subgraphs in Data Streams
[chapter]
2012
Lecture Notes in Computer Science
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We provide the first non-trivial estimator for approximately counting the number of occurrences of an arbitrary subgraph H of constant size in a (large) graph G. ...
Prior to this work, only for a few non-regular graphs estimators were known in case of edge-insertions, leaving the problem of counting general subgraphs in the turnstile model wide open. ...
An Unbiased Estimator for Counting Subgraphs We present a framework for counting general subgraphs. ...
doi:10.1007/978-3-642-31585-5_53
fatcat:dcit3yxswjf2fh6ozojicficxe
Estimating Graphlet Statistics via Lifting
[article]
2018
arXiv
pre-print
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This work introduces a framework for estimating the graphlet count - the number of occurrences of a small subgraph motif (e.g. a wedge or a triangle) in the network. ...
We outline three variants of lifted graphlet counts: the ordered, unordered, and shotgun estimators. ...
This fact enables [19] to provide a local estimator of the stationary probability π (S). ...
arXiv:1802.08736v1
fatcat:lcv4h7mei5ecnh7bcuuvh5xzh4
Adaptive Shrinkage Estimation for Streaming Graphs
[article]
2020
arXiv
pre-print
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In this work, we consider the fundamental problem of estimating the higher-order dependencies using adaptive sampling. ...
We propose a novel adaptive, single-pass sampling framework and unbiased estimators for higher-order network analysis of large streaming networks. ...
E[ S J,t ] = 1 and hence n i,t = J∈Hi,t S J,t is an unbiased estimator of the local subgraph count n i,t for all i ∈ K t . ...
arXiv:1908.01087v4
fatcat:nvtj6266mvfsxmpkzj7jlza4iq
Locating highly connected clusters in large networks with HyperLogLog counters
[article]
2021
arXiv
pre-print
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Our proposed approach adapts the HyperBall algorithm to localize regions with a high density of small subgraph patterns in large graphs in a memory-efficient manner. ...
We use this method to evaluate three measures of subgraph connectivity: conductance, the number of triangles, and transitivity. ...
The bottleneck of the HYPERBALL-type algorithms for local graphlet count is the initialisation that requires, for each node v, the exact count of the graphlets that involve v. ...
arXiv:2101.04610v1
fatcat:ybdwwab5nbfpbgtnepntdewtiu
Efficient estimation of graphlet frequency distributions in protein-protein interaction networks
2006
Bioinformatics
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Local structure of networks can be measured by the frequency distribution of graphlets, small connected non-isomorphic induced subgraphs. ...
This measure of local structure has been used to show that high-confidence PPI networks have local structure of geometric random graphs. ...
The research was supported by the Natural Sciences and Engineering Research Council of Canada, the Ontario Graduate Scholarship Program and IBM Canada. Conflict of Interest: none declared. ...
doi:10.1093/bioinformatics/btl030
pmid:16452112
fatcat:vf5ju3gypvdsnlgc2azzrhskoe
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