Algorithms Analysis Practice Test 2025 - Free Algorithms Practice Questions and Study Guide

A complete graph is specifically defined as a graph in which every pair of distinct vertices is connected by a unique edge. This characteristic signifies that if there are n vertices in the complete graph, there will be exactly n(n-1)/2 edges, each joining two different vertices. This unique and comprehensive connectivity is what sets complete graphs apart from other types of graphs.

The connection between each pair of vertices ensures that the graph is fully interconnected, allowing for maximum connectivity. In terms of graph theory, this means that there are no isolated vertices and no missed connections; every vertex has a direct edge to every other vertex.

The other options, while they may relate to certain properties of graphs, do not accurately define a complete graph. For example, having each vertex connect to at least one other vertex can describe various types of graphs, including ones that are not complete. Similarly, directed edges pertain to directed graphs, and having all vertices of the same degree refers to regular graphs, which can exist independently of the complete graph structure.