Examining evolving structural networks using minimal cycle similarity networks: applications to stick-slip granular dynamics

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A complex network consisting of nodes and links evolves through time by destroying old links and creating new links. Existing nodes can also be destroyed and new nodes can be created. We introduce a framework based on the evolution of the minimal cycle topology whereby the changes in the network can be characterized through properties of a new similarity network. We demonstrate the methodology by focussing on the local mesoscopic cycle evolution within structural contact networks of quasistatically deforming dense granular materials. At each stage of a prescribed loading program (e.g. biaxial compression subject to constant confining pressure boundary conditions) the assembly of granular particles is represented by a contact network. This complex network is rich in cycle topologies and for each particle we compare the changes to its local mesoscopic cycle topology across a specified strain (or temporal) interval. A similarity network constructed using close topological distance of cycle changes between particles summarizes the structural evolution. Properties of the similarity network including centrality measures and motif structures helps to reveal deformation associated with stick-slip behaviour.