How to create an edge list dataframe from a adjacency matrix in Python?

Using rename_axis + reset_index + melt:

df.rename_axis('Source')\
  .reset_index()\
  .melt('Source', value_name='Weight', var_name='Target')\
  .query('Source != Target')\
  .reset_index(drop=True)

  Source Target  Weight
0       B      A     1.0
1       C      A     0.8
2       D      A     0.0
3       A      B     0.5
4       C      B     0.0
5       D      B     0.0
6       A      C     0.5
7       B      C     0.0
8       D      C     1.0
9       A      D     0.0
10      B      D     0.0
11      C      D     0.2

melt has been introduced as a function of the DataFrame object as of 0.20, and for older versions, you'd need pd.melt instead:

v = df.rename_axis('Source').reset_index()
df = pd.melt(
      v, 
      id_vars='Source', 
      value_name='Weight', 
      var_name='Target'
).query('Source != Target')\
 .reset_index(drop=True)

Timings

x = np.random.randn(1000, 1000)
x[[np.arange(len(x))] * 2] = 0

df = pd.DataFrame(x)

%%timeit
df.index.name = 'Source'
df.reset_index()\
  .melt('Source', value_name='Weight', var_name='Target')\
  .query('Source != Target')\
  .reset_index(drop=True)

1 loop, best of 3: 139 ms per loop

# Wen's solution

%%timeit
df.values[[np.arange(len(df))]*2] = np.nan
df.stack().reset_index()

10 loops, best of 3: 45 ms per loop

Two approaches using NumPy tools -

Approach #1

def edgelist(df):
    a = df.values
    c = df.columns
    n = len(c)
    
    c_ar = np.array(c)
    out = np.empty((n, n, 2), dtype=c_ar.dtype)
    
    out[...,0] = c_ar[:,None]
    out[...,1] = c_ar
    
    mask = ~np.eye(n,dtype=bool)
    df_out = pd.DataFrame(out[mask], columns=[['Source','Target']])
    df_out['Weight'] = a[mask]
    return df_out

Sample run -

In [155]: df
Out[155]: 
     A    B    C    D
A  0.0  0.5  0.5  0.0
B  1.0  0.0  0.0  0.0
C  0.8  0.0  0.0  0.2
D  0.0  0.0  1.0  0.0

In [156]: edgelist(df)
Out[156]: 
   Source Target  Weight
0       A      B     0.5
1       A      C     0.5
2       A      D     0.0
3       B      A     1.0
4       B      C     0.0
5       B      D     0.0
6       C      A     0.8
7       C      B     0.0
8       C      D     0.2
9       D      A     0.0
10      D      B     0.0
11      D      C     1.0

Approach #2

# https://stackoverflow.com/a/46736275/ @Divakar
def skip_diag_strided(A):
    m = A.shape[0]
    strided = np.lib.stride_tricks.as_strided
    s0,s1 = A.strides
    return strided(A.ravel()[1:], shape=(m-1,m), strides=(s0+s1,s1))

# https://stackoverflow.com/a/48234170/ @Divakar
def combinations_without_repeat(a):
    n = len(a)
    out = np.empty((n,n-1,2),dtype=a.dtype)
    out[:,:,0] = np.broadcast_to(a[:,None], (n, n-1))
    out.shape = (n-1,n,2)
    out[:,:,1] = onecold(a)
    out.shape = (-1,2)
    return out  

cols = df.columns.values.astype('S1')
df_out = pd.DataFrame(combinations_without_repeat(cols))
df_out['Weight'] = skip_diag_strided(df.values.copy()).ravel()

Runtime test

Using @cᴏʟᴅsᴘᴇᴇᴅ's timing setup :

In [704]: x = np.random.randn(1000, 1000)
     ...: x[[np.arange(len(x))] * 2] = 0
     ...: 
     ...: df = pd.DataFrame(x)

# @cᴏʟᴅsᴘᴇᴇᴅ's soln
In [705]: %%timeit
     ...: df.index.name = 'Source'
     ...: df.reset_index()\
     ...:   .melt('Source', value_name='Weight', var_name='Target')\
     ...:   .query('Source != Target')\
     ...:   .reset_index(drop=True)
10 loops, best of 3: 67.4 ms per loop

# @Wen's soln
In [706]: %%timeit
     ...: df.values[[np.arange(len(df))]*2] = np.nan
     ...: df.stack().reset_index()
100 loops, best of 3: 19.6 ms per loop

# Proposed in this post - Approach #1
In [707]: %timeit edgelist(df)
10 loops, best of 3: 24.8 ms per loop

# Proposed in this post - Approach #2
In [708]: %%timeit
     ...: cols = df.columns.values.astype('S1')
     ...: df_out = pd.DataFrame(combinations_without_repeat(cols))
     ...: df_out['Weight'] = skip_diag_strided(df.values.copy()).ravel()
100 loops, best of 3: 17.4 ms per loop

Using NetworkX 2.x API:

import networkx as nx

In [246]: G = nx.from_pandas_adjacency(df, create_using=nx.MultiDiGraph())

In [247]: G.edges(data=True)
Out[247]: OutMultiEdgeDataView([('A', 'B', {'weight': 0.5}), ('A', 'C', {'weight': 0.5}), ('B', 'A', {'weight': 1.0}), ('C', 'A', {'weight': 0.8}), ('C', 'D', {
'weight': 0.2}), ('D', 'C', {'weight': 1.0})])

In [248]: nx.to_pandas_edgelist(G)
Out[248]:
  source target  weight
0      A      B     0.5
1      A      C     0.5
2      B      A     1.0
3      C      A     0.8
4      C      D     0.2
5      D      C     1.0