Graph ADT_5
For a given graph g :

We are implementing the following graph using the data structure shown below:
adj = { 'u': {'v': 'e', 'w': 'g'}, 'v': {'u': 'e', 'w': 'f'}, 'w': {'u': 'g', 'v': 'f', 'z': 'h'}, 'z': {'w': 'h'}}

This graph is implemented using an Adjacency Matrix representation.

Question

Graph ADT_5
For a given graph g :

We are implementing the following graph using the data structure shown below:
adj = {    'u': {'v': 'e', 'w': 'g'},    'v': {'u': 'e', 'w': 'f'},    'w': {'u': 'g', 'v': 'f', 'z': 'h'},    'z': {'w': 'h'}}

This graph is implemented using an Adjacency Matrix representation.

BlackTom AI · Accepted Answer

First, let's identify the form of the given data structure. The graph is described as adj = { 'u': {'v': 'e', 'w': 'g'}, 'v': {'u': 'e', 'w': 'f'}, 'w': {'u': 'g', 'v': 'f', 'z': 'h'}, 'z': {'w': 'h'}}. This is a mapping from each vertex to another mapping of neighboring vertices and associated values. Such a structure is characteristic of an adjacency list representation (potentially with weights or labels on edges), because it directly lists, for every vertex, which other vertices are adjacent and stores some value for each edge.

Option 1: True. Stating that the graph is implemented using an Adjacency Matrix would be inaccurate here. An adjacency matrix would be a two-dimensional array (or nested lists/dense matrix) indexed by vertex order, with rows and columns corresponding to vertices and cell values indicating presence (and optionally weight) of an edge. There is no 2D matrix shown; instead we have a nested dictionary structure.

Option 2: False. This option aligns with the actual structure: the provided representation is not an adjacency matrix but an adjacency list (with extra edge values). The key differences are that the adjacency list stores, for each vertex, a list (or map) of its neighbors, while an adjacency matrix would require a fixed-size 2D table with all vertex pairs, typically containing 0/1 or weights.

To further illustrate, if we had vertices [u, v, w, z], an adjacency matrix would be a 4x4 grid where cell (u, v) would indicate the edge between u and v, cell (u, w) the edge between u and w, and so on, using a consistent indexing scheme. In contrast, the given adj structure encodes edges directly in nested dictionaries, e.g., adj['u'] contains the entries for its neighbors 'v' and 'w'. This confirms it is not an adjacency matrix.

In summary, option 1 asserts a matrix-based implementation, which is not supported by the data structure shown, and option 2 correctly reflects that the structure is an adjacency list (with edge values) rather than a matrix.

Graph ADT_5 For a given graph g : We are implementing the following graph using the data structure shown below: adj = { 'u': {'v': 'e', 'w': 'g'}, 'v': {'u': 'e', 'w': 'f'}, 'w': {'u': 'g', 'v': 'f', 'z': 'h'}, 'z': {'w': 'h'}} This graph is implemented using an Adjacency Matrix representation.

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