Degree distribution, rank-size distribution, and leadership persistence in mediation-driven 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 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.
- 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;
- Rank-size distribution;
- Degree distribution;
- Scale-free;
- Power-law;
- Mediation-driven attachment networks;
- Winner takes it all;
- Physics - Physics and Society;
- Condensed Matter - Statistical Mechanics;
- Computer Science - Social and Information Networks
- E-Print:
- 4 pages, 6 figures