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

Abstract

We develop a simplified implementation of the Hoshen-Kopelman cluster counting
algorithm adapted for honeycomb networks.

In our implementation of the algorithm we assume that all nodes in the network
are occupied and links between nodes can be intact or broken.

The algorithm counts how many clusters there are in the network and determines
which nodes belong to each cluster. The network information is stored into
two sets of data. The first one is related to the connectivity of the nodes and
the second one to the state of links. The algorithm finds all clusters in only
one scan across the network and thereafter cluster relabeling operates on a
vector whose size is much smaller than the size of the network. Counting
the number of clusters of each size, the algorithm determines the cluster
size probability distribution from which the mean cluster size parameter can
be estimated. Although our implementation of the Hoshen-Kopelman algorithm
works only for networks with a honeycomb (hexagonal) structure, it
can be easily changed to be applied for networks with arbitrary connectivity
between the nodes (triangular, square, etc.).

The proposed adaptation of  the Hoshen-Kopelman cluster counting algorithm
is applied to studying the thermal degradation of a graphene-like honeycomb
membrane by means of Molecular Dynamics simulation with a Langevin thermostat.

ACM Computing Classification System (1998): F.2.2, I.5.3.