Intersection Graph - Formal Definition

Formal Definition

Formally, an intersection graph is an undirected graph formed from a family of sets

Si, i = 0, 1, 2, ...

by creating one vertex vi for each set Si, and connecting two vertices vi and vj by an edge whenever the corresponding two sets have a nonempty intersection, that is,

E(G) = {{vi, vj} | Si ∩ Sj ≠ ∅}.

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