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Threshold functions for small subgraphs in simple graphs and multigraphs [article]

Gwendal Collet, Élie de Panafieu, Danièle Gardy, Bernhard Gittenberger, Vlady Ravelomanana
2018 arXiv   pre-print
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, for various models of random (multi)graphs.  ...  One application is to scale-free multigraphs, where the degree distribution follows a power law, for which we show how to obtain the asymptotic number of copies of a given subgraph and give as an illustration  ...  We thank a referee for careful reading which lead to substantial improvements of the original paper.  ... 
arXiv:1807.05772v1 fatcat:q6dea5zjmrhhdetphb6arpkmra

Threshold functions for small subgraphs: an analytic approach [article]

Gwendal Collet, Élie de Panafieu, Danièle Gardy, Bernhard Gittenberger, Vlady Ravelomanana
2017 arXiv   pre-print
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees.  ...  Our approach relies heavily on analytic combinatorics and on the notion of patchwork to describe the possible overlapping of copies.  ...  Small subgraphs in graphs with degree constraints We consider now (n, m, D)-graphs, which are (n, m)-graphs where all vertices have their degree in the set D.  ... 
arXiv:1705.08768v1 fatcat:wwwwa4zy5zer7jvfuj46ah44p4

Mining frequent subgraphs in multigraphs

Vijay Ingalalli, Dino Ienco, Pascal Poncelet
2018 Information Sciences  
This complex data can be represented as a multigraph structure -a generic and rich graph representation.  ...  In this paper, we propose a novel frequent subgraph mining approach MuGraM that can be applied to multigraphs.  ...  simple graphs.  ... 
doi:10.1016/j.ins.2018.04.001 fatcat:zinpz6rjgrdxtpkjmvwwfoxjuq

A New Multi-graph Transformation Method for Frequent Approximate Subgraph Mining

Niusvel Acosta Mendoza
2018 Revista Cubana de Ciencias Informáticas  
This paper aims at accelerating the mining process, thus a more efficient method is proposed for transforming multi-graphs into simple graphs and vice versa without losing topological or semantic information  ...  Frequent approximate subgraph (FAS) mining has been successfully applied in several science domains, because in many applications, approximate approaches have achieved better results than exact approaches  ...  Acknowledgment This work was partly supported by the National Council of Science and Technology of Mexico (CONACyT) through the scholarship grant 287045.  ... 
doaj:fd95475a0a8b48ae8513ba3496740d55 fatcat:ozwvmwjo2neqlbq6bovmqjomuy

Properties of random graphs with hidden color

Bo Söderberg
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
Cluster size statistics are derived with generating function techniques, yielding a well-defined percolation threshold. Explicit rules are derived for the enumeration of small subgraphs.  ...  We investigate in some detail a recently suggested general class of ensembles of sparse undirected random graphs based on a hidden stub-coloring, with or without the restriction to nondegenerate graphs  ...  Nowicki on the complications associated with subgraph distributions is gratefully acknowledged. This work was in part supported by the Swedish Foundation for Strategic Research.  ... 
doi:10.1103/physreve.68.026107 pmid:14525049 fatcat:ybht4tqslfgjhfvb4fmypia4ne

Non-Vertex-Balanced Factors in Random Graphs [article]

Stefanie Gerke, Andrew McDowell
2013 arXiv   pre-print
We prove part of a conjecture by Johansson, Kahn and Vu JKV regarding threshold functions for the existence of an H-factor in a random graph .  ...  We prove that the conjectured threshold function is correct for any graph H which is not covered by its densest subgraphs.  ...  Theorem 1 . 2 . 12 Fix a multigraph H(which may be a simple graph H).  ... 
arXiv:1304.3000v1 fatcat:gaqkr46pbngrbhxiglvxtp6xie

Page 2289 of Mathematical Reviews Vol. , Issue 83f [page]

1983 Mathematical Reviews  
~*/' is the threshold function for the property that G,.mny COMtains a balanced graph H as a subgraph. He proves  ...  Rudolf Halin (Hamburg) Bollobas, Bela 83f:05065 Threshold functions for small Math. Proc. Cambridge Philos. Soc. 90 (1981), no. 2, 197-206.  ... 

Multi-graph-view Learning for Graph Classification

Jia Wu, Zhibin Hong, Shirui Pan, Xingquan Zhu, Zhihua Cai, Chengqi Zhang
2014 2014 IEEE International Conference on Data Mining  
In order to learn classification models, we propose a multi-graph-view bag learning algorithm (MGVBL), which aims to explore subgraph features from multiple graphviews for learning.  ...  By enabling a joint regularization across multiple graph-views, and enforcing labeling constraints at the bag and graph levels, MGVBL is able to discover most effective subgraph features across all graph-views  ...  DP140100545 and DP140102206.  ... 
doi:10.1109/icdm.2014.97 dblp:conf/icdm/WuHPZCZ14 fatcat:2ax3yvc4mjg3nhw4uh6kwuj63i

On Generalized Random Railways

HANS GARMO, SVANTE JANSON, MICHA KAROSKI
2004 Combinatorics, probability & computing  
It is shown that the probability that the generalized railway is functioning is linear in the proportion of switches. Thus there is no threshold phenomenon for this property.  ...  We consider a random generalized railway defined as a random 3-regular multigraph where some vertices are regarded as switches not allowing traffic between any pair of attached edges.  ...  We thank Pontus Andersson for pointing out an error in a preliminary version of this paper.  ... 
doi:10.1017/s0963548303005820 fatcat:mxvcbasc4neq5nehnsk2m4mmze

On a colored Turán problem of Diwan and Mubayi [article]

Ander Lamaison, Alp Müyesser, Michael Tait
2020 arXiv   pre-print
Diwan and Mubayi also asked for an analogue of Erdős-Stone-Simonovits theorem in this context.  ...  We prove the following asymptotic characterization of the extremal threshold in terms of the chromatic number χ(H) and the reduced maximum matching number ℳ(H) of H. mex(n, H)=(1- 1/2(χ(H)-1) - Ω(ℳ(H)/  ...  For all d ∈ (0, 1] and ∆, s ≥ 1, there exist an ε 0 and an L such that if G is an r-colored graph, H is an r-colored multigraph with maximum degree ∆ in each color, and R is a multicolor regularity multigraph  ... 
arXiv:2010.02953v1 fatcat:gejv3wr4bveorhn6nc3bwjwr7m

An Enhancement of Grami Based on Threshold Policy for Pattern Big Graphs

2020 VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE  
This paper follows the Grami structure for the analysis of frequent subgraph mining and also introduces the 20% threshold policy for the enhancement of the directed pattern graphs.  ...  Many databases consider small graphs for solving complex problems. The classification of graph depends upon the application requirement.  ...  In the former case, small graphs are considered to represent different transactions, such small graphs are created using the database.  ... 
doi:10.35940/ijitee.c9106.019320 fatcat:tf6eladipjekhh4dgveytwsgsm

Discovering subjectively interesting multigraph patterns

Sarang Kapoor, Dhish Kumar Saxena, Matthijs van Leeuwen
2020 Machine Learning  
Though this proposal is inspired by our previous related research for simple graphs (having only single edges), the properties of multigraphs make this transition challenging.  ...  Firstly, we propose a novel subjective interestingness measure for patterns in both undirected and directed multigraphs.  ...  Acknowledgements This research has been conducted as part of an Indo-Dutch project titled 'A Systems approach towards Data Mining and Predictions in Airline Operation' (SAPPAO), Grant No.: MIT-861-MID.  ... 
doi:10.1007/s10994-020-05873-9 fatcat:26z3svzlubbi7igrs5vryoe3xa

The Pebbling Threshold of the Square of Cliques [article]

Airat Bekmetjev, Glenn Hurlbert
2004 arXiv   pre-print
In this paper we find the pebbling threshold of the sequence of squares of cliques, improving upon an earlier result of Boyle and verifying an important instance of a probabilistic version of Graham's  ...  Given an initial configuration of pebbles on a graph, one can move pebbles in pairs along edges, at the cost of one of the pebbles moved, with the objective of reaching a specified target vertex.  ...  Acknowledgments The authors wish to thank Graham Brightwell for useful hallway conversations during his visit to ASU.  ... 
arXiv:math/0406157v1 fatcat:hopkdzvhw5ezza4gm3dux4lz4a

The pebbling threshold of the square of cliques

A. Bekmetjev, G. Hurlbert
2008 Discrete Mathematics  
In this paper we find the pebbling threshold of the sequence of squares of cliques, improving upon an earlier result of Boyle and verifying an important instance of a probabilistic version of Graham's  ...  Given an initial configuration of pebbles on a graph, one can move pebbles in pairs along edges, at the cost of one of the pebbles moved, with the objective of reaching a specified target vertex.  ...  Acknowledgments The authors wish to thank Graham Brightwell for useful hallway conversations during his visit to ASU.  ... 
doi:10.1016/j.disc.2007.08.012 fatcat:hzbtuvhelncqta6qvcrycm5ype

Error Floor Approximation for LDPC Codes in the AWGN Channel [article]

Brian K. Butler, Paul H. Siegel
2013 arXiv   pre-print
We develop a refined linear model, based on the work of Sun and others, that accurately predicts error floors caused by elementary tapping sets for saturating decoders.  ...  We employ an LLR-domain SPA decoder that does not saturate near-certain messages and find the error rates of our decoder to be lower by at least several orders of magnitude.  ...  Also, we thank Yang Han and William Ryan for providing the QC parity check matrix.  ... 
arXiv:1202.2826v2 fatcat:4a7u4qhrojcsfhhclhfbsc4r3y
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