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Open Cluster


An open cluster in bond percolation is a connected component of the graph formed by the open edges. If omega:E->{0,1} records the state of every edge of a graph G=(V,E), the open clusters are the connected components of

 (V,{e in E:omega(e)=1}).

The open cluster containing a vertex v is commonly denoted C(v). Percolation occurs when an infinite open cluster exists.


See also

Connected Component, Percolation, Random-Cluster Model

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References

Grimmett, G. Percolation, 2nd ed. Berlin, Germany: Springer-Verlag, 1999.

Cite this as:

Weisstein, Eric W. "Open Cluster." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OpenCluster.html

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