Complex Networks: effect of subtle changes in nature of randomness

TL;DR

This paper investigates how subtle modifications in the randomness of Watts Strogatz and Euclidean network models influence their structural properties and phase transition points, revealing nuanced effects on network behavior.

Contribution

It introduces specific subtle changes in randomness within two network classes and analyzes their impact on network exponents and phase transitions, providing new insights into network robustness.

Findings

Finite differences in exponents observed in Watts Strogatz networks.

Shift in phase transition points in Euclidean networks.

Models are equivalent at extreme parameter values.

Abstract

In two different classes of network models, namely, the Watts Strogatz type and the Euclidean type, subtle changes have been introduced in the randomness. In the Watts Strogatz type network, rewiring has been done in different ways and although the qualitative results remain same, finite differences in the exponents are observed. In the Euclidean type networks, where at least one finite phase transition occurs, two models differing in a similar way have been considered. The results show a possible shift in one of the phase transition points but no change in the values of the exponents. The WS and Euclidean type models are equivalent for extreme values of the parameters; we compare their behaviour for intermediate values.