= Entropy bound for graphs with isolated-vertex-free intersections
{title2=$|\mathcal F|\leq2^{n(n-2)/2}$}
If every pair of <graphs> in a family on $[n]$ has a <graph intersection> without an <isolated vertex>, the family has at most $2^{n(n-2)/2}$ members. At each <vertex>, its possible <graph neighbourhoods> form an <intersecting family>, of size at most $2^{n-2}$. Every <edge> occurs in two such neighbourhood projections. <Shearer inequality> bounds twice the full <information entropy> by the sum of their <information entropies>.
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