We are not able to resolve this OAI Identifier to the repository landing page. If you are the repository manager for this record, please head to the Dashboard and adjust the settings.
This paper studies Random and Evolving Apollonian networks (RANs and EANs), in d dimension for any d = 2, i.e. dynamically evolving random d dimensional simplices looked as graphs inside an initial d-dimensional simplex. We determine the limiting degree distribution in RANs and show that it follows a power law tail with exponent t = (2d - 1)/(d - 1). We further show that the degree distribution in EANs converges to the same degree distribution if the simplex-occupation parameter in the nth step of the dynamics is qn→0 and \sum_{n=0}^\infty q_n = \infty.ThisresultgivesarigorousprooffortheconjectureofZhangetal[31]thatEANstendtoshowsimilarbehaviorasRANsoncetheoccupationparameterq \rightarrow 0$. We also determine the asymptotic behavior of shortest paths in RANs and EANs for arbitrary d dimensions. For RANs we show that the shortest path between two uniformly chosen vertices (typical distance), the flooding time of a uniformly picked vertex and the diameter of the graph after n steps all scale as constant times log n. We determine the constants for all three cases and prove a central limit theorem for the typical distances. We prove a similar CLT for typical distances in EANs
Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.