Basic Weighted Adjacency Matrix

00:00 4 marks

Consider a graph with 4 vertices. Construct a weighted adjacency matrix where the weight between vertices i and j is given by w(i,j) = i + j if they are connected, and 0 otherwise. Assume that the graph is complete (i.e., every pair of distinct vertices is connected). Provide the resulting matrix.

Hint Hint

Hint

Recall that a complete graph has an edge between every pair of vertices and use the given weight formula.

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Complete Answer

The weighted adjacency matrix is [[0, 3, 4, 5], [3, 0, 5, 6], [4, 5, 0, 7], [5, 6, 7, 0]].

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