Abstract
Complex network growth across diverse fields of science is hypothesized to be driven in the main by a combination of preferential attachment and node fitness processes. For measuring the respective influences of these processes, previous approaches make strong and untested assumptions on the functional forms of either the preferential attachment function or fitness function or both. We introduce a Bayesian statistical method called PAFit to estimate preferential attachment and node fitness without imposing such functional constraints that works by maximizing a log-likelihood function with suitably added regularization terms. We use PAFit to investigate the interplay between preferential attachment and node fitness processes in a Facebook wall-post network. While we uncover evidence for both preferential attachment and node fitness, thus validating the hypothesis that these processes together drive complex network evolution, we also find that node fitness plays the bigger role in determining the degree of a node. This is the first validation of its kind on real-world network data. But surprisingly the rate of preferential attachment is found to deviate from the conventional log-linear form when node fitness is taken into account. The proposed method is implemented in the R package PAFit.
Highlights
Complex network growth across diverse fields of science is hypothesized to be driven in the main by a combination of preferential attachment and node fitness processes
Edge dynamics in a given model produce networks with structural features similar on average to those observed in real networks, it is within the bounds of possibility that the same mechanisms are operative in their real-world counterparts
We report the first evidence of the co-existence of Preferential attachment (PA) and fitness mechanisms, or, in other words, rich-get-richer and fit-get-richer effects in the growth of a Facebook wall-post dataset[54]
Summary
Complex network growth across diverse fields of science is hypothesized to be driven in the main by a combination of preferential attachment and node fitness processes. While we uncover evidence for both preferential attachment and node fitness, validating the hypothesis that these processes together drive complex network evolution, we find that node fitness plays the bigger role in determining the degree of a node This is the first validation of its kind on real-world network data. Network scientists rely on a class of network models, known as generative network models, or sometimes evolving or growing network models, to investigate possible mechanisms underlying complex network formation In this modelling paradigm, complex networks are generated by means of the incremental addition and deletion of nodes and edges to a seed network over a long sequence of time-steps. Edge dynamics in a given model produce networks with structural features similar on average to those observed in real networks, it is within the bounds of possibility that the same mechanisms are operative in their real-world counterparts
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