Degree distribution, ranksize distribution, and leadership persistence in mediationdriven attachment networks
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 mediationdriven attachment (MDA) network exhibits powerlaw P(k) ∼^{k  γ(m)} with a spectrum of exponents depending on m. To appreciate the contrast between MDA and BarabásiAlbert (BA) networks, we then discuss their ranksize 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 powerlaw 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.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 March 2017
 DOI:
 10.1016/j.physa.2016.11.001
 arXiv:
 arXiv:1411.3444
 Bibcode:
 2017PhyA..469...23H
 Keywords:

 Leadership persistence probability;
 Ranksize distribution;
 Degree distribution;
 Scalefree;
 Powerlaw;
 Mediationdriven attachment networks;
 Winner takes it all;
 Physics  Physics and Society;
 Condensed Matter  Statistical Mechanics;
 Computer Science  Social and Information Networks
 EPrint:
 4 pages, 6 figures