Python script that creates the product graph, which consists of pairs of identically labeled nodes and edges from G1 and G2.

product_graph.py

import networkx as nx
import matplotlib.pyplot as plt
"""
Implements Product Graph operator proposed in https://sites.cs.ucsb.edu/~xyan/tutorial/GraphKernels.pdf.
"""

def product_graph(G1,G2):
	G = nx.lexicographic_product(G1,G2)
	PG = nx.Graph()
	for n in G.nodes():
		if n[0] == n[1]:
			PG.add_node(n)

	for e in G.edges.data('weight', default=0):
		v1 = e[0][0]
		w1 = e[0][1]
		v2 = e[1][0]
		w2 = e[1][1]
		label = e[2]
		if v1==w1 and v2==v2 and G1.get_edge_data(v1,v2,default=0) and G2.get_edge_data(w1,w2,default=0) and \
		   G1.get_edge_data(v1,v2,default=0) == G2.get_edge_data(w1,w2,default=0):
			PG.add_edge((v1,w1),(v2,w2),weight=label)

	return PG


if __name__=='__main__':
	G1=nx.Graph()
	G2=nx.Graph()

	G1.add_nodes_from([('a'),'b','c'])
	G1.add_weighted_edges_from([('a','b',1),('b','c',2),('a','c',3)])

	G2.add_nodes_from(['a','b','c','d'])
	G2.add_weighted_edges_from([('a','b',1),('b','c',2),('c','d',3),('a','d',4)])
	PG = product_graph(G1,G2)
	
	nx.draw(PG,with_labels=True)
	labels = nx.get_edge_attributes(PG,'weight')
	pos=nx.spring_layout(PG)
	nx.draw_networkx_edge_labels(PG,pos,edge_labels=labels)
	plt.show()