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:
C_G6
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.
Syntax: networkx.complete_graph(n)
Parameters:
- 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)
Parameters:
- 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.
Approach:
- 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.
Example 1:
Python3
# import required module import networkx # create object G = networkx.complete_graph(6) # illustrate graph networkx.draw(G, node_color = 'green', node_size = 1500) |
Output:
Output
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.
Example 2:
Python3
# import required module import networkx # create object G = networkx.complete_graph(10) # illustrate graph networkx.draw(G, node_color = 'green', node_size = 1500) |
Output:
Advantages and Disadvantages:
Advantages of using a complete graph in social network analysis include:
- Simplicity: Complete graphs are a simple structure that can be easily understood, making it easy to extract insights from the data.
- High connectivity: All nodes in a complete graph are connected to each other, which makes it easy to model all possible interactions between the nodes.
- Representing fully connected groups: Complete graphs can be used to represent groups where all members are fully connected, such as small teams or communities.
Disadvantages of using a complete graph in social network analysis include:
Limited representation of real-world networks: Complete graphs are a highly simplified representation of real-world networks, which may not accurately reflect the complexity and diversity of the relationships in a network.
High computational cost: Complete graphs have a high number of edges, which can make it computationally expensive to analyze and visualize.
Limited scalability: Complete graphs are not suitable for very large networks as the number of edges increases exponentially with the number of nodes.
Reference:
“Python NetworkX: A Practical Overview” by Shai Vaingast is a good reference book for learning NetworkX and its application in social network analysis. The book covers the basics of NetworkX and its use in solving real-world problems such as community detection, centrality measures, and graph visualization. It also includes examples of creating and analyzing complete graphs using NetworkX.
