Minimum Spanning Trees (Edexcel A-Level Further Mathematics): Quizzes

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Networks & Matrices
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In a network, what do weights on edges typically represent?

Distances, costs, or capacities

In an adjacency matrix, what does aij=1a_{ij} = 1 indicate?

Edge exists between ii and jj

In a weighted matrix, what value represents no edge between vertices ii and jj?

\infty

What does a zero entry on the diagonal of a matrix typically mean?

No self-loop at that vertex

For undirected graphs, what property must the adjacency matrix have?

Symmetric: aij=ajia_{ij} = a_{ji}

What is the first step when drawing a network from a matrix?

Label vertices using rows/columns

When drawing a network from a matrix, which entries indicate edges?

Non-zero entries

In an adjacency matrix, what value indicates no edge?

00

What is the key difference between weighted and adjacency matrices?

Weighted uses weights, adjacency uses 1/0

For directed graphs, what property may not hold in the matrix?

Symmetry of entries

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