Similarity Networks of the Functional Evolution of Cycles in Structural Networks

We construct networks summarizing similarity of local mesoscopic cycle evolution within structural contact networks of quasistatically deforming dense granular materials. In essence, at each stage of the deformation, a contact network is created and a minimal cycle basis is calculated. For each grain we compare its local mesoscopic cycle topology across a specified strain (or temporal) interval and summarize this evolution in a similarity network. We propose a prescription for finding a suitably sized strain interval. Concentrating on times when stickslip
or jamming-unjamming behaviour is evident we relate properties of the similarity networks (e.g., community structures) to areas of failure throughout the material.