The shortest distance in random multi‐type intersection graphs

Barbour, A. D.; Reinert, Gesine

doi:10.1002/rsa.20351

Cited by 23 publications

(42 citation statements)

References 25 publications

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“…Distances between vertices of a random intersection graph (distance distribution, typical distances, diameter) have been considered in Barbour and Reinert (2011), Bloznelis (2009), Rybarczyk (2011a.…”

Section: Formentioning

confidence: 99%

Recent Progress in Complex Network Analysis: Properties of Random Intersection Graphs

Bloznelis

Godehardt

Jaworski

et al. 2015

Data Science, Learning by Latent Structures, and Knowledge Discovery

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Experimental results show that in large complex networks (such as internet, social or biological networks) there exists a tendency to connect elements which have a common neighbor. In theoretical random graph models, this tendency is described by the clustering coefficient being bounded away from zero. Complex networks also have power-law degree distributions and short average distances (small world phenomena). These are desirable features of random graphs used for modeling real life networks. We survey recent results concerning various random intersection graph models showing that they have tunable clustering coefficient, a rich class of degree distributions including power-laws, and short average distances.

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Section: Formentioning

confidence: 99%

Recent Progress in Complex Network Analysis: Properties of Random Intersection Graphs

Bloznelis

Godehardt

Jaworski

et al. 2015

Data Science, Learning by Latent Structures, and Knowledge Discovery

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show abstract

“…= for a given digraph D , and we note that multitype graphs can be used to study the multi-species in ecology and have been deeply studied (see [26] [27]). So these generalizations of competition graphs may be more realistic and more interesting.…”

Section: D C Dmentioning

confidence: 99%

Competition Numbers of Several Kinds of Triangulations of a Sphere

Zhao¹,

Fang²,

Cui³

et al. 2017

OJDM

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It is hard to compute the competition number for a graph in general and characterizing a graph by its competition number has been one of important research problems in the study of competition graphs. Sano pointed out that it would be interesting to compute the competition numbers of some triangulations of a sphere as he got the exact value of the competition numbers of regular polyhedra. In this paper, we study the competition numbers of several kinds of triangulations of a sphere, and get the exact values of the competition numbers of a 24-hedron obtained from a hexahedron by adding a vertex in each face of the hexahedron and joining the vertex added in a face with the four vertices of the face, a class of dodecahedra constructed from a hexahedron by adding a diagonal in each face of the hexahedron, and a triangulation of a sphere with ( ) 3 2 n n ≥ vertices.

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“…= for a given digraph D , and we note that multitype graphs can be used to study the multi-species in ecology and have been deeply studied, see [23] [24]. So these generalizations of competition graphs may be more realistic and more interesting.…”

Section: ) Ifmentioning

confidence: 99%

Competition Numbers of a Kind of Pseudo-Halin Graphs

Cao¹,

Cui²,

Ye³

et al. 2017

OJDM

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For any graph G , G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number ( ) k G of a graph G is defined to be the smallest number of such isolated vertices. In general, it is hard to compute the competition number ( ) k G for a graph G and characterizing a graph by its competition number has been one of important research problems in the study of competition graphs. A 2-connected planar graph G with minimum degree at least 3 is a pseudo-Halin graph if deleting the edges on the boundary of a single face 0 f yields a tree. It is a Halin graph if the vertices of 0 f all have degree 3 in G . In this paper, we compute the competition numbers of a kind of pseudo-Halin graphs.

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The shortest distance in random multi‐type intersection graphs

Cited by 23 publications

References 25 publications

Recent Progress in Complex Network Analysis: Properties of Random Intersection Graphs

Recent Progress in Complex Network Analysis: Properties of Random Intersection Graphs

Competition Numbers of Several Kinds of Triangulations of a Sphere

Competition Numbers of a Kind of Pseudo-Halin Graphs

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