从 Python 中的掩码网格制作图形

Question

I've got a 'mask' numpy 2D array with ones and zeros, eg

array([[0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0],
       [0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0],
       [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0],
       [1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1],
       [0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0],
       [1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1],
       [0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0],
       [0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0],
       [0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0],
       [1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1],
       [0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0],
       [1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1],
       [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0],
       [0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0],
       [0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0]])

My task is to convert this matrix into a connected graph with the zeros as nodes connected with their direct neighbors, that is, for example, the graph in this case would contain several graphs (not connected with each other), like:

*         *---*
|
*---*            *
|                |
*                *
etc...

So basically each zero here is a node and edges are paths to other zeros which are their direct neighbors (on the top, bottom, right or left). Direction of edges does matter! Edges are either vertical or horizontal, as in the input matrix. My ultimate goal is to use the resulting graph / collection of graphs to perform a number of tests:

• connectivity of all nodes
• max and min length of edges (in each orientation)
• etc.

I've found out the excellent networkx library which seems to be able to generate graphs from arrays, but the reference says it can only treat nd-arrays or pandas dataframes as 'adjacency' matrices and not as direct graph representations as in my case.

Answer 1

You can convert your representation of the graph to an adjacency matrix representation by finding the indices of all the zeros and calculating the distance between them. After the transformation, you can pass the graph to networkx's functions. Here is an example of a code that implements this idea and uses it on a small portion of your array: