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

## DOI:

https://doi.org/10.55630/sjc.2014.8.363-388## Keywords:

Cluster Counting Algorithm, Honeycomb Network, Molecular Dynamics Simulation## 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.