convert a simple matrix to incidence matrix with python

Question

i want to make graph network from incidence Matrix, but i don't have an incidence Matrix, i have just a simple Matrix.so my question is: how to convert a simple Matrix to a incidence Matrix to draw a graph network with python?

Answer 1

I hope this is helpful, the output is shown at the end

import numpy as np
import networkx as nx #version 2.2
import matplotlib.pyplot as plt
import pandas as pd

# matrix goes here
Mat = [
    [0,0,-1,0,0],
    [1,1,-1,-1,0],
    [1,-1,0,0,0],
    [1,0,0,-1,0],
    [1,0,1,-1,1]
]

A = pd.DataFrame(Mat)
#refine rowname and colnames
nodes = ["a","b","c","d","e"]

A.index = nodes
A.columns = nodes

#create graph
G0 = nx.from_pandas_adjacency(A)

#create weight labels
combs = {}
adjc = G0.adj
for i in adjc:
    suba = adjc[i]
    for j in suba:
        combs[(i,j)] = suba[j]['weight']
        
#define network structure i.e shell        
nx.draw_shell(G0, with_labels=True )
nx.draw_networkx_edge_labels(G0, pos=nx.shell_layout(G0), edge_labels=combs)
plt.draw()

Answer 2

Both matrices are adjacency matrices. The most important thing is to know that they are different datatypes:

import pandas as pd
import numpy as np

adjacency = [[0,0,-1,0,0], [1,1,-1,-1,0], [1,-1,0,0,0], [1,0,0,-1,0], [1,0,1,-1,1]]
df = pd.DataFrame(adjacency, columns = ['A','B','C','D','E'], index = ['A','B','C','D','E'])

This results in different methods of handling incidencies as well as different structure of graph:

As you can note easily, first method uses automatic assignment of node labels to indices 0, 1, 2, 3, 4.

Another surprising facts: you don't need to collect weights manually. They are stored in weight attribute of edges.

Usage:

You can access edge attributes with nx.get_edge_attributes(G, 'weight'). This is my simplified version of diagram structure:

G = nx.from_pandas_adjacency(df)
pos = nx.circular_layout(G)
nx.draw(G, pos, with_labels=True, bbox = dict(fc="lightgreen", ec="black", boxstyle="circle", lw=3),
    width=2, arrowsize=30)
nx.draw_networkx_edge_labels(G, pos, edge_labels = nx.get_edge_attributes(G, 'weight'))
plt.show()