A random graph model is proposed which is a special case of sparse random graphs with given degree sequences which involves only a small number of parameters, called logsize and log-log growth rate, which capture some universal characteristics of massive graphs.Expand

It is shown that for certain families of random graphs with given expected degrees the average distance is almost surely of order log n/log d́, where d̃ is the weighted average of the sum of squares of the expected degrees.Expand

Abstract. We consider a family of random graphs with a given expected degree sequence. Each edge is chosen independently with probability proportional to the product of the expected degrees of its… Expand

Graph theory in the information age Old and new concentration inequalities A generative model--the preferential attachment scheme Duplication models for biological networks Random graphs with given… Expand

It is shown that LeaderRank outperforms PageRank in terms of ranking effectiveness, as well as robustness against manipulations and noisy data, which suggest that leaders who are aware of their clout may reinforce the development of social networks, and thus the power of collective search.Expand

A random graph model is proposed which is a special case of sparserandom graphs with given degree sequences which satisfy a power law and involves only a small number of parameters, called logsize and log-log growth rate, which capture some universal characteristics of massive graphs.Expand

We modify the definition of Ricci curvature of Ollivier of Markov chains on graphs to study the properties of the Ricci curvature of general graphs, Cartesian product of graphs, random graphs, and… Expand

It is shown that for certain families of random graphs with given expected degrees, the average distance is almost surely of order log n/ logd̃ where d̃ is the weighted average of the sum of squares of the expected degrees.Expand