A complete graph also called a Full Graph it is a graph that has n vertices where the degree of each vertex is n-1. In other words, each vertex is connected with every other vertex.
Example: Complete Graph with 6 edges:
Properties of Complete Graph:
- The degree of each vertex is n-1.
- The total number of edges is n(n-1)/2.
- All possible edges in a simple graph exist in a complete graph.
- It is a cyclic graph.
- The maximum distance between any pair of nodes is 1.
- The chromatic number is n as every node is connected to every other node.
- Its complement is an empty graph.
We will use the networkx module for realizing a Complete graph. It comes with an inbuilt function networkx.complete_graph() and can be illustrated using the networkx.draw() method. This module in Python is used for visualizing and analyzing different kinds of graphs.
- N: Number of nodes in complete graph.
- Returns an networkx graph complete object.
- Nodes are indexed from zero to n-1.
Used to realize the graph by passing graph object.
networkx.draw(G, node_size, node_color)
- G: It refers to the complete graph object
- node_size: It refers to the size of nodes.
- node_color: It refers to color of the nodes.
- We will import the required module networkx.
- Then we will create a graph object using networkx.complete_graph(n).
- Where n specifies n number of nodes.
- For realizing graph, we will use networkx.draw(G, node_color = ’green’, node_size=1500)
- The node_color and node_size arguments specify the color and size of graph nodes.
The output of the above program gives a complete graph with 6 nodes as output as we passed 6 as an argument to the complete_graph function.
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