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All 8 Flashcards — Adjacency matrices
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Question
What is an adjacency matrix?
Answer
A square matrix where rows and columns are the vertices (same order); entry (i,j) = the number of edges from vertex i to vertex j.
Question
How can you tell an undirected adjacency matrix from a directed one?
Answer
An undirected graph gives a SYMMETRIC matrix (edges go both ways); a directed graph is usually not symmetric.
Question
What does the (i,j) entry of Aⁿ tell you?
Answer
The number of walks of length n (n edges, repeats allowed) from vertex i to vertex j.
Question
Does 'length of a walk' mean distance?
Answer
No — length = the number of EDGES used. Use the weighted/distance matrix for actual distance.
Question
Where do you read 'closed walks' (return to start) in Aⁿ?
Answer
On the DIAGONAL — entry (i,i) of Aⁿ counts walks of length n that start and end at vertex i.
Question
How do you build a distance (weighted) matrix?
Answer
Replace each 1 in the adjacency matrix with the weight (distance/cost/time) of that edge; keep 0 (or blank/∞) where there is no edge.
Question
How do you count length-4 routes from X to Y on a GDC?
Answer
Enter A, compute A⁴, then read the entry in row X, column Y.
Question
For an undirected graph, what does the (i,i) entry of A² equal?
Answer
The degree of vertex i (the number of edges meeting it) — 'out and straight back'.
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Topic 3.15 hub
Adjacency matrices (HL only)
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