A complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. In other words, every vertex in a complete graph is adjacent to all other vertices. A complete graph is denoted by the symbol K_n, where n is the number of vertices in the graph. Some characteristics of a complete graph are:

• Connectedness: A complete graph is a connected graph, which means that there exists a path between any two vertices in the graph.

• Count of edges: Every vertex in a complete graph has a degree (n-1), where n is the number of vertices in the graph. So the total number of edges in a complete graph with n vertices is n*(n-1)/2.

• Symmetry: Every edge in a complete graph is symmetric with each other, meaning that it is undirected and connects two vertices in the same way.

• Transitivity: A complete graph is a transitive graph, which means that if vertex A is connected to vertex B and vertex B is connected to vertex C, then vertex A is also connected to vertex C.

• Regularity: A complete graph is a regular graph, meaning that every vertex has the same degree.

Complete graphs are used in various fields, including computer networking and geometry.