Beyond the Steady-State: Analytical Study of Network Growth at Arbitrary Times, for Arbitrary Initial Conditions

2014/11/03 by Babak Fotouhi, Fotouhi, Babak
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #cs.SI #physics.soc-ph

paper · pdf · doi:10.48550/arxiv.1411.0715

arxiv created 2014/11/03 · arxiv updated 2014/11/05

Abstract

In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the infinite-size limit). Consequently, empirical studies also seek to verify the steady-state prediction in real data. The caveat concomitant with confining the analysis to this time regime is that no real system has infinite size; most real growing networks are far from the steady state. This underlines the importance of finite-size analysis. In this paper, we consider the shifted-linear preferential attachment as an illustrative example of arbitrary-time network growth analysis. We obtain the degree distribution for arbitrary initial conditions at arbitrary times. We corroborate our theoretical predictions with Monte Carlo simulations.

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