An Adaptation of the Hoshen-Kopelman Cluster Counting Algorithm for Honeycomb Networks

Abstract

We develop a simplified implementation of the Hoshen-Kopelman cluster countingalgorithm adapted for honeycomb networks.In our implementation of the algorithm we assume that all nodes in the networkare occupied and links between nodes can be intact or broken. The algorithm counts how many clusters there are in the network and determineswhich nodes belong to each cluster. The network information is stored intotwo sets of data. The first one is related to the connectivity of the nodes andthe second one to the state of links. The algorithm finds all clusters in onlyone scan across the network and thereafter cluster relabeling operates on avector whose size is much smaller than the size of the network. Countingthe number of clusters of each size, the algorithm determines the clustersize probability distribution from which the mean cluster size parameter canbe estimated. Although our implementation of the Hoshen-Kopelman algorithmworks only for networks with a honeycomb (hexagonal) structure, itcan be easily changed to be applied for networks with arbitrary connectivitybetween the nodes (triangular, square, etc.).The proposed adaptation of the Hoshen-Kopelman cluster counting algorithmis applied to studying the thermal degradation of a graphene-like honeycombmembrane by means of Molecular Dynamics simulation with a Langevin thermostat.ACM Computing Classification System (1998): F.2.2, I.5.3.