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Adjacency Matrix

Definition: Let G = <V, E> be a directed graph with |V| = n. The adjacency matrix of G is the boolean n * n matrix M where M(x, y) = true if and only if <x, y> in E:

adjacency(G) :=

let V = G0, E = G1:

such M in V x V -> {true, false}:

(forall x in V, y in V: M(x, y) = true <=> <x, y> in E).

Matrix representation from graph.