ITPEC FE Morning October 2021 Question 4

Adjacency Matrix for Directed Graphs — map directed edges to a matrix where row = source, column = destination.

Read each edge from the graph and mark 1 in the matrix:

• •Directed edge from i to j → matrix[i][j] = 1
• •No edge → 0
• •Self-loop (edge from a node to itself) → diagonal entry = 1

Edges in this graph:
- A → B
- B → A
- B → C

Resulting matrix:

Why not others:
- (a) — adds self-loops on A, B, C and a non-existent A→C edge
- (b) — incorrectly sets A→B = 0, adds C→A and C→B edges
- (c) — adds self-loops on A, B, C and swaps some connections

Key rule: In a directed graph adjacency matrix, matrix[i][j] = 1 means there is an edge from vertex i to vertex j. Curved arrows between two nodes are mutual edges, not self-loops.

AI-generated — may contain errors