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sider a model of a growing directed network similar to Price's m Section 13.1, but without preferential attachment. That is, nodes ar e to the growing network and each has c outgoing edges, but those ed xisting nodes chosen uniformly at random, without regard for degre e properties.

sider a model of a growing directed network similar to Price's m Section 13.1, but without preferential attachment. That is, nodes ar e to the growing network and each has c outgoing edges, but those ed xisting nodes chosen uniformly at random, without regard for degre e properties.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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13.6 Consider a model of a growing directed network similar to Price's model de- scribed in Section 13.1, but without preferential attachment. That is, nodes are added one by one to the growing network and each has c outgoing edges, but those edges now attach to existing nodes chosen uniformly at random, without regard for degrees or any other node properties. a) Derive master equations, the equivalent of Eqs. (13.7) and (13.8), that govern the distribution of in-degrees q in the limit of large network size. b) Hence show that in the limit of large size the in-degrees have an exponential distribution pg = C rª, where C is a normalization constant and r = c/(c + 1).
Transcribed Image Text:13.6 Consider a model of a growing directed network similar to Price's model de- scribed in Section 13.1, but without preferential attachment. That is, nodes are added one by one to the growing network and each has c outgoing edges, but those edges now attach to existing nodes chosen uniformly at random, without regard for degrees or any other node properties. a) Derive master equations, the equivalent of Eqs. (13.7) and (13.8), that govern the distribution of in-degrees q in the limit of large network size. b) Hence show that in the limit of large size the in-degrees have an exponential distribution pg = C rª, where C is a normalization constant and r = c/(c + 1).
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