scholarly journals Perspectives on exponential random graphs

2020 ◽  
pp. 59-81
Author(s):  
Ryan DeMuse ◽  
Mei Yin
Keyword(s):  
Random Graphs ◽  
Exponential Random Graphs

scholarly journals Phase transitions in exponential random graphs

2013 ◽  
Vol 23 (6) ◽  
pp. 2458-2471 ◽  
Author(s):  
Charles Radin ◽  
Mei Yin
Keyword(s):  
Phase Transitions ◽  
Random Graphs ◽  
Exponential Random Graphs

Finite-size effects in exponential random graphs

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
A Gorsky ◽  
O Valba
Keyword(s):  
Random Graphs ◽  
Ground State ◽  
Size Effects ◽  
Chemical Potential ◽  
Network Flows ◽  
Finite Size ◽  
Critical Value ◽  
Star Model ◽  
Finite Size Effects ◽  
Exponential Random Graphs

Abstract In this article, we show numerically the strong finite-size effects in exponential random graphs. Particularly, for the two-star model above the critical value of the chemical potential for triplets a ground state is a star-like graph with the finite set of hubs at network density $p<0.5$ or as the single cluster at $p>0.5$. We find that there exists the critical value of number of nodes $N^{*}(p)$ when the ground state undergoes clear-cut crossover. At $N>N^{*}(p),$ the network flows via a cluster evaporation to the state involving the small star in the Erdős–Rényi environment. The similar evaporation of the cluster takes place at $N>N^{*}(p)$ in the Strauss model. We suggest that the entropic trap mechanism is relevant for microscopic mechanism behind the crossover regime.

scholarly journals Mixing time of exponential random graphs

2011 ◽  
Vol 21 (6) ◽  
pp. 2146-2170 ◽  
Author(s):  
Shankar Bhamidi ◽  
Guy Bresler ◽  
Allan Sly
Keyword(s):  
Random Graphs ◽  
Mixing Time ◽  
Exponential Random Graphs

scholarly journals Exponential Random Graphs as Models of Overlay Networks

2009 ◽  
Vol 46 (1) ◽  
pp. 199-220 ◽  
Author(s):  
M. Draief ◽  
A. Ganesh ◽  
L. Massoulié
Keyword(s):  
Communication Networks ◽  
Random Graphs ◽  
Degree Distribution ◽  
Overlay Networks ◽  
Analytic Solution ◽  
Mean Value ◽  
Asymptotic Results ◽  
Graph Expansion ◽  
Exponential Random Graphs ◽  
Random Failures

In this paper we give an analytic solution for graphs withnnodes andE=cnlognedges for which the probability of obtaining a given graphGisµn(G) = exp (-β∑i=1ndi2), wherediis the degree of nodei. We describe how this model appears in the context of load balancing in communication networks, namely peer-to-peer overlays. We then analyse the degree distribution of such graphs and show that the degrees are concentrated around their mean value. Finally, we derive asymptotic results for the number of edges crossing a graph cut and use these results (i) to compute the graph expansion and conductance, and (ii) to analyse the graph resilience to random failures.

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