Complete graph

A simple graph in which every pair of distinct vertices is joined by an edge. A complete graph on n vertices has n(n−1)/2 edges.

Graph (discrete mathematics): A structure consisting of vertices and edges that connect pairs of vertices. A complete graph is a special case of this general structure.
Degree (graph theory): The number of edges incident to a vertex in a graph. Every vertex in a complete graph on n vertices has degree n−1.
Traveling salesman problem: The optimization problem of finding a shortest tour that visits each city once and returns to its start. Its standard graph model connects every city pair, often with weighted complete graphs.
Empty graph: A graph with vertices and no edges. It is the edge-free extreme opposite to a complete graph on the same vertices.
Vertex (graph theory): An individual point in a graph, also called a node. Completeness requires every pair of distinct vertices to be adjacent.
Handshaking lemma: The theorem that the sum of vertex degrees in a finite graph equals twice its number of edges. It gives the edge count from the uniform degree n−1.
Network topology: The arrangement of connections among nodes in a communication or transportation network. A complete topology connects every pair directly, maximizing connectivity at high link cost.
Path graph: A graph whose vertices can be arranged in a single path with edges only between consecutive vertices. A path has only enough edges to connect the vertices in sequence.
Edge (graph theory): A connection between two vertices in a graph. Each pair of vertices in a complete graph has exactly one edge.
Clique (graph theory): A set of vertices in a graph whose members are pairwise adjacent. The entire vertex set of a complete graph is a clique.

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