Consider the following directed graph: A / \ E D \ / C | B E->A D->A C->E C->D B->C Which of the following is the adjacency matrix for this graph?
Question
Consider the following directed graph:
A
/
E D
\ /
C
|
B
E->A
D->A
C->E
C->D
B->C
Which of the following is the adjacency matrix for this graph?
Solution
An adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the adjacency matrix, rows represent source vertices and columns represent destination vertices.
Given the directed graph and the directions of the edges, the adjacency matrix would be:
A B C D E A 0 0 0 0 0 B 0 0 1 0 0 C 0 0 0 1 1 D 1 0 0 0 0 E 1 0 0 0 0
This matrix is read as:
- A does not have any outgoing edges (row A has all 0s).
- B has an edge to C (in row B, column C is 1).
- C has edges to D and E (in row C, columns D and E are 1).
- D has an edge to A (in row D, column A is 1).
- E has an edge to A (in row E, column A is 1).
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