Consider a network given by the adjacency matrix a ij = a ji = 1 with probability
Question:
Consider a network given by the adjacency matrix aij = aji = 1 with probability p and aij = aji = 0 with probability 1 − p.
(a) In the limit of large N and fixed pN, compute the degree distribution and calculate the connectivity.
(b) Now exclude the nodes of degree zero and neglect degree correlations. Use the distribution derived in (a) in the limit of large N and Np fixed to express the average return time ri for the nodes of non-zero degree in terms of Ei(pN), where Ei(pN) denotes the exponential integral.
(c) Compare the expression in (b) with the estimate one obtains by the definition of ri in Eq. (8.99), replacing ki by the average degree and L by the average number of links. Consider the limit Np → 0 and N ≫ 1.
Eq. (8.99)
Step by Step Answer:
Complexity Science The Study Of Emergence
ISBN: 9781108834766
1st Edition
Authors: Henrik Jeldtoft Jensen