= Bond percolation
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In independent bond percolation with parameter $p$, every <edge> of a <graph> is open with <probability> $p$ and closed with <probability> $1-p$. The choices are <independent random variables> with a <Bernoulli distribution>. All <vertices> remain present; only the usable connections change. The <percolation clusters> are the <connected components of a graph> formed by the open <edges>, including isolated <vertices>.
A specified simple <graph path> with $m$ <edges> is an <open path> with <probability> $p^m$, by <independence>. Connecting its endpoints is a different <event>: other <graph paths> may also connect them. The four-<edge> example in <percolation theory> makes that distinction explicit. Interpreting open <edges> as usable channels makes the model useful for connectivity questions; it does not by itself assign a travel time, flow rate, or capacity to a channel.
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