Networkx to_edgelist() and from_edgelist() give me different graphs for an edgelist generated from one graph

The following code

import networkx as nx
import numpy as np

# Create a graph

random_graph = nx.erdos_renyi_graph(10, 0.5, seed=2)

G = random_graph

# Get the edge list representation
edge_list = nx.to_edgelist(G)

# Create a new graph from the edge list
new_G = nx.from_edgelist(edge_list)

# Check if the graphs are the same
print("Original Graph Adjacency Matrix:")
print(np.array(nx.adjacency_matrix(G).todense()))


print("New Graph Adjacency Matrix:")
print(np.array(nx.adjacency_matrix(new_G).todense()))


# Print adjacency matrices of the original and reconstructed graphs
original_adj_matrix = np.array(nx.adjacency_matrix(G).todense())
new_adj_matrix = np.array(nx.adjacency_matrix(new_G).todense())

# Compare adjacency matrices with a tolerance for floating-point differences
if np.allclose(original_adj_matrix, new_adj_matrix, atol=1e-8):
    print("The original and reconstructed graphs are the same.")
else:
    print("The original and reconstructed graphs are different.")

Produces the following output:

Original Graph Adjacency Matrix:
[[0 0 0 1 1 0 0 0 1 0]
 [0 0 0 0 1 1 1 0 0 0]
 [0 0 0 0 1 1 1 1 1 1]
 [1 0 0 0 1 0 0 0 1 1]
 [1 1 1 1 0 1 1 0 0 0]
 [0 1 1 0 1 0 1 0 0 0]
 [0 1 1 0 1 1 0 0 0 0]
 [0 0 1 0 0 0 0 0 1 0]
 [1 0 1 1 0 0 0 1 0 0]
 [0 0 1 1 0 0 0 0 0 0]]
New Graph Adjacency Matrix:
[[0 1 1 1 0 0 0 0 0 0]
 [1 0 1 1 0 0 0 0 0 1]
 [1 1 0 0 1 1 1 1 0 0]
 [1 1 0 0 0 0 0 1 1 0]
 [0 0 1 0 0 1 1 0 0 0]
 [0 0 1 0 1 0 1 1 0 0]
 [0 0 1 0 1 1 0 1 0 0]
 [0 0 1 1 0 1 1 0 1 1]
 [0 0 0 1 0 0 0 1 0 0]
 [0 1 0 0 0 0 0 1 0 0]]
The original and reconstructed graphs are different.

Am I doing something wrong?

I was expecting the methods to_edgelist() and from_edgelist() to produce the same graphs, however they are both very different.

On different runs, the original and the new adjacency matrix remain the same, but they don’t match.

>Solution :

Your issue is due to the non consistent order of the nodes.

As noted in the documentation of adjacency_matrix, the nodelist parameter controls the order of the rows/columns:

nodelist
list, optional

The rows and columns are ordered according to the nodes in nodelist. If nodelist is None, then the ordering is produced by
G.nodes().

Thus you should use a defined order:

nodes = sorted(G)

edge_list = nx.to_edgelist(G, nodelist=nodes)
new_G = nx.from_edgelist(edge_list)

np.array_equal(nx.adjacency_matrix(G, nodelist=nodes).todense(),
               nx.adjacency_matrix(new_G, nodelist=nodes).todense())
# True