Visualizing the composition two of graph using networkx

In this article, we are going to see how to visualize the composition two of the graph using networkx. If we are given two graphs A and B then their composition can be found by performing union operation on node-set and edge-set of A and B.

Simply if an edge is contained between any two vertices in any of the initial graphs it will be contained in the composition of those graphs.

Example:

Initial Graph G:

G

Initial Graph H:

H

Result of Composition of G and H:

Composition(G,H)

Explanation: If we name nodes in both graphs G and H using integers then we will clearly observe that node and edge set of G will be superset of H and hence their union gives G in return.

Example 2:

Initial Graph G:

G

Initial Graph H:

H

Result of Composition of G and H:

R

Explanation: We can see that all the edges which are in graph G are present in graph H except the node between first and third node from right therefore doing composition of G and H adds all edges from G and H into the result.

Important points about Compose function:

• H attributes take precedent over G attributes.
• The graph returned is of the same type as G.
• G and H should either be both directed or both undirected.
• G and H must both be graphs or multigraphs

Realizing Composition using Python :

We will use networkx.compose() function for our task to do composition of 2 graphs.

Syntax: compose(G, H)

• G: It is a networkx Graph object which is passed as an argument to compose function.
• H: It is also an networkx Graph object which is passed as an argument to compose function.

Result of compose function will be union of edge and vertices set of G and H.

Approach:

• We will import networkx with an alias nx.
• Create a sample graph object G using path_graph() function.
• Create second sample graph object H using path_graph() function.
• We will then call compose function passing G as an argument.
• We will capture the object returned by compose function in another object R.
• We will then call draw() function passing R as an argument which will display the complement graph.

Code:

Python3

# importing networkx module
import networkx as nx

# creating sample graph object
G = nx.path_graph(7)

# creating sample graph object
H = nx.path_graph(3)

# compose of G and H saving in R
R = nx.compose(G,H)

# calling draw() to visualize the complement graph
nx.draw(R)

Output:

OUTPUT