Correct Answer:
C. Complete graph
The correct answer is Complete graph. In graph theory, a complete graph is defined as a simple undirected graph in which every distinct pair of vertices is connected by a unique edge. This means that for any given node in the graph, there is a direct link or edge to every other node present in that graph. If a graph has 'n' nodes, then in a complete graph, each node will have exactly 'n-1' edges connected to it. Complete graphs represent the maximum possible connectivity between a set of vertices without allowing loops or multiple edges between the same two vertices. They are often denoted by K_n, where 'n' is the number of vertices.
- Directed graph is incorrect because it refers to a graph where the edges have a specific direction, meaning they only allow traversal from one vertex to another in a single specified orientation. A directed graph does not necessarily imply that every node is connected to every other node; it merely describes the nature of the edges.
- Weighted graph is incorrect because it is a graph where each edge has an assigned numerical value or 'weight,' which can represent cost, distance, or capacity. While a complete graph can be weighted, the definition of a weighted graph does not require universal connectivity among all nodes.
- Sparse graph is incorrect because it describes a graph where the number of edges is relatively small compared to the maximum possible number of edges for its given number of vertices. This is the opposite of a complete graph, which has the maximum number of edges possible.