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Visualizing the composition two of graph using networkx

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  • Last Updated : 24 Jan, 2021
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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

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