Complete graph

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The full graph up to .

A complete graph is a term from graph theory and describes a simple graph in which every node is connected to every other node by an edge . The complete graph with nodes is uniquely determined (except for isomorphism ) and is denoted by.

If the set of nodes of the complete graph , then the set of edges is exactly the set of edges between pairs of different nodes .

A complete graph is also its maximal clique .


The complete graphs to are planar . All other complete graphs are not planar according to Kuratowski's theorem , since they contain them as a subgraph.

The number of edges of the complete graph corresponds to the triangle number


The complete graph is a - regular graph : each node has neighbors . Because of this, every node coloring of the graph has colors. Furthermore, it follows that the complete graphs are Eulerian for odd and not for even .

Complete graphs are for Hamiltonian graphs . The complete graph contains different Hamilton circles .


The idea of ​​the complete graph can be transferred to -partite graphs . These are complete if every node of a partition is connected to all nodes of all other partitions. The complete multipartite graph with partition sets containing nodes is called .

If you provide a complete graph with an orientation, you get a tournament graph .


Using free Python - Library NetworkX to complete graphs can be generated. Example:

import networkx as nx
import matplotlib.pyplot as plt

G = nx.complete_graph(15)

nx.draw_circular(G, with_labels=True, font_weight='bold')


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