The degree sequence of a scale-free random graph process
Random Structures & Algorithms
Random Structures & Algorithms
The Diameter of a Scale-Free Random Graph
Combinatorica
The Maximum Degree of the Barabási–Albert Random Tree
Combinatorics, Probability and Computing
Graphs over time: densification laws, shrinking diameters and possible explanations
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Graph evolution: Densification and shrinking diameters
ACM Transactions on Knowledge Discovery from Data (TKDD)
Scale-free graphs of increasing degree
Random Structures & Algorithms
New classes of clustering coefficient locally maximizing graphs
Discrete Applied Mathematics
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We consider a random graph process in which, at each time step, a new vertex is added with m out-neighbours, chosen with probabilities proportional to their degree plus a strictly positive constant. We show that the expectation of the clustering coefficient of the graph process is asymptotically proportional to lognn. Bollobas and Riordan have previously shown that when the constant is zero, the same expectation is asymptotically proportional to (logn)^2n.