On adaptability and "intermediate phase" in randomly connected networks

TL;DR

This paper introduces a model analyzing phase transitions in random networks, revealing an adaptive intermediate phase where the network self-adjusts to reduce stress, with applications in computational problems.

Contribution

The paper presents an analytical model of phase transitions in random networks and links these insights to computational problems like vertex cover and K-SAT.

Findings

Identification of a floppy to rigid transition in networks

Discovery of a self-adaptive intermediate phase

Verification through simulations

Abstract

We present a simple model that enables us to analytically characterize a floppy to rigid transition and an associated self-adaptive intermediate phase in a random bond network. In this intermediate phase, the network adapts itself to lower the stress due to constraints. Our simulations verify this picture. We use these insights to identify applications of these ideas in computational problems such as vertex cover and K-SAT.