scholarly journals The Domination Number of On-line Social Networks and Random Geometric Graphs

2015 ◽  
pp. 150-163 ◽  
Author(s):  
Anthony Bonato ◽  
Marc Lozier ◽  
Dieter Mitsche ◽  
Xavier Pérez-Giménez ◽  
Paweł Prałat
Keyword(s):  
Social Networks ◽  
Domination Number ◽  
Geometric Graphs ◽  
Random Geometric Graphs ◽  
On Line

scholarly journals Domination number within on-line social networks

2021 ◽  
Author(s):  
Marc Lozier
Keyword(s):  
Social Networks ◽  
Domination Number ◽  
Upper Bounds ◽  
Dominating Sets ◽  
Geometric Distance ◽  
New Model ◽  
On Line ◽  
Domination Numbers

There is particular interest in on-line social networks (OSNs) and capturing their properties. The memoryless geometric protean (MGEO-P) model provably simulated many OSN properties. We investigated dominating sets in OSNs and their models. The domination numbers were computed using two algorithms, DS-DC and DS-RAI, for MGEO-P samples and Facebook data, known as the Facebook 100 graphs. We establish sub-linear bounds on the domination numbers for the Facebook 100 graphs, and show that these bounds correlate well with bounds in graphs simulated by MGEO-P. A new model is introduced known as the Distance MGEO-P (DMGEO-P) model. This model incorporates geometric distance to inuence the probability that two nodes are adjacent. Domination number upper bounds were found to be well-correlated with the Facebook 100 graph.

scholarly journals Domination number within on-line social networks

2021 ◽  
Author(s):  
Marc Lozier
Keyword(s):  
Social Networks ◽  
Domination Number ◽  
Upper Bounds ◽  
Dominating Sets ◽  
Geometric Distance ◽  
New Model ◽  
On Line ◽  
Domination Numbers

There is particular interest in on-line social networks (OSNs) and capturing their properties. The memoryless geometric protean (MGEO-P) model provably simulated many OSN properties. We investigated dominating sets in OSNs and their models. The domination numbers were computed using two algorithms, DS-DC and DS-RAI, for MGEO-P samples and Facebook data, known as the Facebook 100 graphs. We establish sub-linear bounds on the domination numbers for the Facebook 100 graphs, and show that these bounds correlate well with bounds in graphs simulated by MGEO-P. A new model is introduced known as the Distance MGEO-P (DMGEO-P) model. This model incorporates geometric distance to inuence the probability that two nodes are adjacent. Domination number upper bounds were found to be well-correlated with the Facebook 100 graph.

scholarly journals Normalized Sombor Indices as Complexity Measures of Random Networks

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 976
Author(s):  
R. Aguilar-Sánchez ◽  
J. Méndez-Bermúdez ◽  
José Rodríguez ◽  
José Sigarreta
Keyword(s):  
Random Matrix ◽  
Adjacency Matrix ◽  
Matrix Theory ◽  
Computational Study ◽  
Random Networks ◽  
Geometric Graphs ◽  
Theory Approach ◽  
Complexity Measures ◽  
Random Geometric Graphs ◽  
Highly Correlated

We perform a detailed computational study of the recently introduced Sombor indices on random networks. Specifically, we apply Sombor indices on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random networks and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the adjacency matrix.

scholarly journals Connectivity in one-dimensional soft random geometric graphs

2020 ◽  
Vol 102 (6) ◽  
Author(s):  
Michael Wilsher ◽  
Carl P. Dettmann ◽  
Ayalvadi Ganesh
Keyword(s):  
Geometric Graphs ◽  
Random Geometric Graphs ◽  
One Dimensional

scholarly journals Convergence Theorems for Some Layout Measures on Random Lattice and Random Geometric Graphs

2000 ◽  
Vol 9 (6) ◽  
pp. 489-511 ◽  
Author(s):  
JOSEP DÍAZ ◽  
MATHEW D. PENROSE ◽  
JORDI PETIT ◽  
MARÍA SERNA
Keyword(s):  
Constant Factor ◽  
Geometric Graphs ◽  
Convergence Theorems ◽  
Linear Arrangement ◽  
Random Lattice ◽  
Random Geometric Graphs ◽  
Unit Square ◽  
Subcritical Regime ◽  
Probabilistic Setting ◽  
Lattice Graphs

This work deals with convergence theorems and bounds on the cost of several layout measures for lattice graphs, random lattice graphs and sparse random geometric graphs. Specifically, we consider the following problems: Minimum Linear Arrangement, Cutwidth, Sum Cut, Vertex Separation, Edge Bisection and Vertex Bisection. For full square lattices, we give optimal layouts for the problems still open. For arbitrary lattice graphs, we present best possible bounds disregarding a constant factor. We apply percolation theory to the study of lattice graphs in a probabilistic setting. In particular, we deal with the subcritical regime that this class of graphs exhibits and characterize the behaviour of several layout measures in this space of probability. We extend the results on random lattice graphs to random geometric graphs, which are graphs whose nodes are spread at random in the unit square and whose edges connect pairs of points which are within a given distance. We also characterize the behaviour of several layout measures on random geometric graphs in their subcritical regime. Our main results are convergence theorems that can be viewed as an analogue of the Beardwood, Halton and Hammersley theorem for the Euclidean TSP on random points in the unit square.

scholarly journals Symmetric motifs in random geometric graphs

2017 ◽  
Vol 6 (1) ◽  
pp. 95-105 ◽  
Author(s):  
Carl P Dettmann ◽  
Georgie Knight
Keyword(s):  
Geometric Graphs ◽  
Random Geometric Graphs
Sign in / Sign up

Export Citation Format

Share Document