Degree distribution, rank-size distribution, and leadership persistence in mediation-driven attachment networks

Md. Kamrul Hassan, Liana Islam and Syed Arefinul Haque

Physica A: Statistical Mechanics and its Applications, 2017, vol. 469, issue C, 23-30

Abstract: We investigate the growth of a class of networks in which a new node first picks a mediator at random and connects with m randomly chosen neighbors of the mediator at each time step. We show that the degree distribution in such a mediation-driven attachment (MDA) network exhibits power-law P(k)∼k−γ(m) with a spectrum of exponents depending on m. To appreciate the contrast between MDA and Barabási–Albert (BA) networks, we then discuss their rank-size distribution. To quantify how long a leader, the node with the maximum degree, persists in its leadership as the network evolves, we investigate the leadership persistence probability F(τ) i.e. the probability that a leader retains its leadership up to time τ. We find that it exhibits a power-law F(τ)∼τ−θ(m) with persistence exponent θ(m)≈1.51∀m in MDA networks and θ(m)→1.53 exponentially with m in BA networks.

Keywords: Leadership persistence probability; Rank-size distribution; Degree distribution; Scale-free; Power-law; Mediation-driven attachment networks; Winner takes it all (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:469:y:2017:i:c:p:23-30

DOI: 10.1016/j.physa.2016.11.001

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