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

Babak Fotouhi

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arXiv · 1411.0715

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

Babak Fotouhi

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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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physics.soc-ph cond-mat.stat-mech cs.SI

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Babak Fotouhi. 2014-11-03. Beyond the Steady-State: Analytical Study of Network Growth at Arbitrary Times, for Arbitrary Initial Conditions. https://arxiv.org/abs/1411.0715

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