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Frailty effects in networks: comparison and identification of individual heterogeneity versus preferential attachment in evolving networks
Author(s) -
Blasio Birgitte Freiesleben de,
Seierstad Taral Guldahl,
Aalen Odd O.
Publication year - 2011
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2010.00746.x
Subject(s) - preferential attachment , generative grammar , mechanism (biology) , identification (biology) , computer science , degree distribution , complex network , variation (astronomy) , human dynamics , protein interaction networks , process (computing) , statistical hypothesis testing , econometrics , artificial intelligence , mathematics , statistics , biology , epistemology , physics , astrophysics , philosophy , world wide web , botany , genetics , protein–protein interaction , operating system
Summary. Preferential attachment is a proportionate growth process in networks, where nodes receive new links in proportion to their current degree. Preferential attachment is a popular generative mechanism to explain the widespread observation of power‐law‐distributed networks. An alternative explanation for the phenomenon is a randomly grown network with large individual variation in growth rates among the nodes (frailty). We derive analytically the distribution of individual rates, which will reproduce the connectivity distribution that is obtained from a general preferential attachment process (Yule process), and the structural differences between the two types of graphs are examined by simulations. We present a statistical test to distinguish the two generative mechanisms from each other and we apply the test to both simulated data and two real data sets of scientific citation and sexual partner networks. The findings from the latter analyses argue for frailty effects as an important mechanism underlying the dynamics of complex networks.