The clustering coefficient of a scale-free random graph
Copyright policy )The clustering coefficient of a scale-free random graph
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 log n/n. Bollobás and Riordan have previously shown that when the constant is zero, the same expectation is asymptotically proportional to ((log n)^2)/n.
17 pages. Submitted
- Brunel University United Kingdom
- Brunel University London United Kingdom
- Kingston University United Kingdom
Applied Mathematics, Barabási–Albert graph, Random graphs (graph-theoretic aspects), clustering coefficient, Barabasi-Albert graph, Clustering coefficient, scale-free graph, 05C80 (Primary) 68R10, 60C05 (Secondary), FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), Barabási-Albert graph, Scale-free graph
Applied Mathematics, Barabási–Albert graph, Random graphs (graph-theoretic aspects), clustering coefficient, Barabasi-Albert graph, Clustering coefficient, scale-free graph, 05C80 (Primary) 68R10, 60C05 (Secondary), FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), Barabási-Albert graph, Scale-free graph
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