Say I have two options for generating the Adjacency Matrix of a network: nx.adjacency_matrix() and my own code. I wanted to test the correctness of my code and came up with some strange inequalities.
Example: a 3x3 lattice network.
import networkx as nx N=3 G=nx.grid_2d_graph(N,N) pos = dict( (n, n) for n in G.nodes() ) labels = dict( ((i,j), i + (N-1-j) * N ) for i, j in G.nodes() ) nx.relabel_nodes(G,labels,False) inds=labels.keys() vals=labels.values() inds.sort() vals.sort() pos2=dict(zip(vals,inds)) plt.figure() nx.draw_networkx(G, pos=pos2, with_labels=True, node_size = 200) This is the visualization:
The adjacency matrix with nx.adjacency_matrix():
B=nx.adjacency_matrix(G) B1=B.todense() [[0 0 0 0 0 1 0 0 1] [0 0 0 1 0 1 0 0 0] [0 0 0 1 0 1 0 1 1] [0 1 1 0 0 0 1 0 0] [0 0 0 0 0 0 0 1 1] [1 1 1 0 0 0 0 0 0] [0 0 0 1 0 0 0 1 0] [0 0 1 0 1 0 1 0 0] [1 0 1 0 1 0 0 0 0]] According to it, node 0 (entire 1st row and entire 1st column) is connected to nodes 5 and 8. But if you look at the image above this is wrong, as it connects to nodes 1 and 3.
Now my code (to be run in in the same script as the above):
import numpy import math P=3 def nodes_connected(i, j): try: if i in G.neighbors(j): return 1 except nx.NetworkXError: return False A=numpy.zeros((P*P,P*P)) for i in range(0,P*P,1): for j in range(0,P*P,1): if i not in G.nodes(): A[i][:]=0 A[:][i]=0 elif i in G.nodes(): A[i][j]=nodes_connected(i,j) A[j][i]=A[i][j] for i in range(0,P*P,1): for j in range(0,P*P,1): if math.isnan(A[i][j]): A[i][j]=0 print(A) This yields:
[[ 0. 1. 0. 1. 0. 0. 0. 0. 0.] [ 1. 0. 1. 0. 1. 0. 0. 0. 0.] [ 0. 1. 0. 0. 0. 1. 0. 0. 0.] [ 1. 0. 0. 0. 1. 0. 1. 0. 0.] [ 0. 1. 0. 1. 0. 1. 0. 1. 0.] [ 0. 0. 1. 0. 1. 0. 0. 0. 1.] [ 0. 0. 0. 1. 0. 0. 0. 1. 0.] [ 0. 0. 0. 0. 1. 0. 1. 0. 1.] [ 0. 0. 0. 0. 0. 1. 0. 1. 0.]] which says that node 0 is connected to nodes 1 and 3. Why does such difference exist? What is wrong in this situation?
2 Answers
Networkx doesn't know what order you want the nodes to be in.
Here is how to call it: adjacency_matrix(G, nodelist=None, weight='weight').
If you want a specific order, set nodelist to be a list in that order. So for example adjacency_matrix(G, nodelist=range(9)) should get what you want.
Why is this? Well, because a graph can have just about anything as its nodes (anything hashable). One of your nodes could have been "parrot" or (1,2). So it stores the nodes as keys in a dict, rather than assuming it's the non-negative integers starting at 0. Dict keys have an arbitrary order.
A more general solution, if your nodes have some logical ordering as is the case if you generate a graph using G=nx.grid_2d_graph(3,3) (which returns tupples from (0,0) to (2,2), or in your example would be to use:
adjacency_matrix(G,nodelist=sorted(G.nodes())) This sorts the returned list of nodes of G and passes it as the nodelist
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