Define an equivalence relation

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Reference no: EM131468927

Question: Consider a possibly disconnected network (N , A). Two nodes i and j in N are said to be connected if there is a path from i to j (recall that paths can traverse arcs backwards or forwards). We write i ∼ j if i and j are connected.

Using the equivalence relation, we can partition N into a collection of subsets of equivalence classes N1, N2,..., Nk such that two nodes are connected if and only if they belong to the same subset. The number k is called the number of connected components.

(b) Show that the rank of the node-arc incidence matrix A is exactly m-k (recall that m is the number of rows of A).

Reference no: EM131468927

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