n adjacency matrix representation of a graph cannot contain information of
A) nodes
B) edges
C) direction of edges
D) parallel edges
The Correct Answer and Explanation is:
Correct Answer: D) parallel edges
An adjacency matrix is a way of representing a graph using a 2D array or matrix. If a graph has n nodes, the adjacency matrix is an n × n matrix where each cell A[i][j] indicates whether there is an edge from node i to node j.
Let’s briefly analyze each option:
- A) Nodes:
The number of rows and columns in the adjacency matrix corresponds to the number of nodes in the graph. Therefore, nodes are inherently represented in the structure of the matrix. - B) Edges:
Edges are indicated by non-zero entries in the matrix. For an unweighted graph, a value of 1 typically indicates the presence of an edge. For a weighted graph, the matrix entries may contain the weight of the edge. - C) Direction of edges:
Directionality is represented in the matrix by asymmetry. If A[i][j] = 1 and A[j][i] = 0, it means there is a directed edge from i to j but not from j to i. So, adjacency matrices can represent directed graphs. - D) Parallel edges:
This is the correct answer.
An adjacency matrix cannot naturally represent parallel edges (i.e., multiple edges between the same pair of nodes). Each cell in the matrix can store only one value per pair of nodes. In an unweighted graph, this is usually just 0 (no edge) or 1 (edge present). Even in weighted graphs, while you can store the total weight of multiple edges, you lose the information about the number and individual properties of each edge. Therefore, the adjacency matrix cannot distinctly represent multiple (parallel) edges between the same pair of nodes.
Conclusion:
Among the given options, the adjacency matrix lacks the ability to represent parallel edges, making D) parallel edges the correct answer.
