Properties of a growing random directed network
Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex UB8 3PH, UK
Corresponding author: a G.J.Rodgers@brunel.ac.uk
Revised: 12 July 2001
Published online: 15 September 2001
We study a number of properties of a simple random growing directed network which can be used to model real directed networks such as the world-wide web and call graphs. We confirm numerically that the distributions of in- and out-degree are consistent with a power law, in agreement with previous analytical results and with empirical measurements from real graphs. We study the distribution and mean of the minimum path length, the high degree nodes, the appearance and size of the giant component and the topology of the nodes outside the giant component. These properties are compared with empirical studies of the world-wide web.
PACS: 02.50.Cw – Probability theory / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 89.75.Hc – Networks and genealogical trees
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001