A Python Implementation of the Newman–Ziff algorithm¶

The pypercolate Python package implements the Newman–Ziff algorithm for bond percolation on graphs.

The elementary unit of computation is the sample state: This is one particular realization with a given number of edges—one member of the microcanonical ensemble. As Newman & Ziff suggest [NZ01], the package evolves a sample state by successively adding edges, in a random but predetermined order. This is implemented as a generator function percolate.percolate.sample_states() to iterate over. Each step of the iteration adds one edge.

A collection of sample states (realizations) evolved in parallel form a microcanonical ensemble at each iteration step. A microcanonical ensemble is hence a collection of different sample states (realizations) but with the same number of edges (occupation number). The percolate.percolate.microcanonical_averages() generator function evolves a microcanonical ensemble. At each step, it calculates the cluster statistics over all realizations in the ensemble. The percolate.percolate.microcanonical_averages_arrays() helper function collects these statistics over all iteration steps into single numpy arrays.

Finally, the percolate.percolate.canonical_averages() function calculates the statistics of the canonical ensemble from the microcanonical ensembles.

The percolate.percolate.sample_states() generator handles cluster joining by the networkx.utils.union_find.UnionFind data structure.