How to color nodes in a adjacency graph with different colors?

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Let us consider a binary adjacency matrix $M$. We want to color the nodes of corresponding adjacency graph with 4 different colors such that two adjacent nodes have different colors. How to find 4 lists of nodes with different colors?

M = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 1,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0,

        1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0,

        0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 

       0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 

       0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0,

        1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,

        0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 

       0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1,

        1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 

       1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0,

        0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 

       0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 

       0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

        1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0,

        1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 

       0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 

       0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0}, {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 

       1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 

       0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0,

        1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 

       0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 

       0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 

       1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0,

        0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 

       0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0,

        0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0,

        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0,

        0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

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edited Dec 3 at 23:39

Henrik Schumacher

47k466134

asked Dec 3 at 23:26

dipak narayanan

1016

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edited Dec 3 at 23:39

Henrik Schumacher

47k466134

asked Dec 3 at 23:26

dipak narayanan

1016

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edited Dec 3 at 23:39

Henrik Schumacher

47k466134

asked Dec 3 at 23:26

dipak narayanan

1016

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       0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0,

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       0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,

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       0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

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       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 

       0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}}

graphics graphs-and-networks color partitions

edited Dec 3 at 23:39

Henrik Schumacher

47k466134

asked Dec 3 at 23:26

dipak narayanan

1016

edited Dec 3 at 23:39

Henrik Schumacher

47k466134

asked Dec 3 at 23:26

dipak narayanan

1016

edited Dec 3 at 23:39

Henrik Schumacher

47k466134

edited Dec 3 at 23:39

Henrik Schumacher

47k466134

edited Dec 3 at 23:39

Henrik Schumacher

47k466134

asked Dec 3 at 23:26

dipak narayanan

1016

asked Dec 3 at 23:26

dipak narayanan

1016

asked Dec 3 at 23:26

dipak narayanan

1016

add a comment |

2 Answers
2

active

oldest

votes

up vote
7
down vote

accepted

That's easy with Szabolcs' IGraph/M package:

Needs["IGraphM`"];

G = AdjacencyGraph[M];

colors = ColorData[97] /@ Range[4];

Graph[G,

 VertexStyle ->Thread[Range[VertexCount[G]] -> colors[[IGKVertexColoring[G, 4][[1]]]]

 ]

enter image description here

Alternatively, one can also use IGMinimumVertexColoring[G]; it shows that three colors are already sufficient for this graph.

Alternatively, the style can also be applied with IGVertexMap:

Graph[G, GraphStyle -> "BasicBlack", VertexSize -> 1.5] //

  IGVertexMap[

    ColorData[97],

    VertexStyle -> IGMinimumVertexColoring

  ]

enter image description here

edited Dec 4 at 10:24

Szabolcs

158k13432926

answered Dec 3 at 23:37

Henrik Schumacher

47k466134

I also need the list of nodes in each color. I prefer almost equal number of nodes in different colors.
– dipak narayanan
Dec 4 at 8:11

1

@dipaknarayanan Look up GroupBy: GroupBy[ Transpose[{VertexList[G], IGMinimumVertexColoring[G]}], Last -> First ]
– Szabolcs
Dec 4 at 9:28

add a comment |

up vote
5
down vote

You can also use the function MinimumVertexColoring from the Combinatorica package:

Needs["Combinatorica`"]

mvc = MinimumVertexColoring[FromAdjacencyMatrix@m];

colors = MapIndexed[#2[[1]] -> # &, ColorData[97] /@ mvc] ;

AdjacencyGraph[m, VertexSize -> 3/2, System`VertexStyle -> colors]

enter image description here

answered Dec 4 at 2:47

kglr

175k9197402

but I must have 4 colors and prefer almost equal number of nodes in different colors. And also the list of nodes in each color
– dipak narayanan
Dec 4 at 8:09

2

@dipak This "but" comes a bit late. Please, be explicit about your constraints the next time you ask a question. Hidden constraints are extremely frustrating for people who try to help you.
– Henrik Schumacher
Dec 4 at 9:08

1

@dipaknarayanan For that I suggest you research how to do graph colouring through integer programming and see if you want include your requirements as a constraint.
– Szabolcs
Dec 4 at 9:40

@kglr Are you still on M9? If you ever upgrade to 10.0+ and would like to contribute to IGraph/M, let me know. There is a lot that you could help with (it's not longer just an igraph interface). Unfortunately, IGraph/M won't work in the cloud version because of the C++ dependencies.
– Szabolcs
Dec 4 at 15:19

@Szabolcs, just upgraded to v11 a few weeks ago. I have installed IGraph/M and reading the documentation now. I would be happy to try my hand to help with what is needed.
– kglr
Dec 4 at 17:01

|
show 8 more comments

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

up vote
7
down vote

accepted

That's easy with Szabolcs' IGraph/M package:

Needs["IGraphM`"];

G = AdjacencyGraph[M];

colors = ColorData[97] /@ Range[4];

Graph[G,

 VertexStyle ->Thread[Range[VertexCount[G]] -> colors[[IGKVertexColoring[G, 4][[1]]]]

 ]

enter image description here

Alternatively, one can also use IGMinimumVertexColoring[G]; it shows that three colors are already sufficient for this graph.

Alternatively, the style can also be applied with IGVertexMap:

Graph[G, GraphStyle -> "BasicBlack", VertexSize -> 1.5] //

  IGVertexMap[

    ColorData[97],

    VertexStyle -> IGMinimumVertexColoring

  ]

enter image description here

edited Dec 4 at 10:24

Szabolcs

158k13432926

answered Dec 3 at 23:37

Henrik Schumacher

47k466134

I also need the list of nodes in each color. I prefer almost equal number of nodes in different colors.
– dipak narayanan
Dec 4 at 8:11

1

@dipaknarayanan Look up GroupBy: GroupBy[ Transpose[{VertexList[G], IGMinimumVertexColoring[G]}], Last -> First ]
– Szabolcs
Dec 4 at 9:28

add a comment |

up vote
7
down vote

accepted

That's easy with Szabolcs' IGraph/M package:

Needs["IGraphM`"];

G = AdjacencyGraph[M];

colors = ColorData[97] /@ Range[4];

Graph[G,

 VertexStyle ->Thread[Range[VertexCount[G]] -> colors[[IGKVertexColoring[G, 4][[1]]]]

 ]

enter image description here

Alternatively, one can also use IGMinimumVertexColoring[G]; it shows that three colors are already sufficient for this graph.

Alternatively, the style can also be applied with IGVertexMap:

Graph[G, GraphStyle -> "BasicBlack", VertexSize -> 1.5] //

  IGVertexMap[

    ColorData[97],

    VertexStyle -> IGMinimumVertexColoring

  ]

enter image description here

edited Dec 4 at 10:24

Szabolcs

158k13432926

answered Dec 3 at 23:37

Henrik Schumacher

47k466134

I also need the list of nodes in each color. I prefer almost equal number of nodes in different colors.
– dipak narayanan
Dec 4 at 8:11

1

@dipaknarayanan Look up GroupBy: GroupBy[ Transpose[{VertexList[G], IGMinimumVertexColoring[G]}], Last -> First ]
– Szabolcs
Dec 4 at 9:28

add a comment |

up vote
7
down vote

accepted

That's easy with Szabolcs' IGraph/M package:

Needs["IGraphM`"];

G = AdjacencyGraph[M];

colors = ColorData[97] /@ Range[4];

Graph[G,

 VertexStyle ->Thread[Range[VertexCount[G]] -> colors[[IGKVertexColoring[G, 4][[1]]]]

 ]

enter image description here

Alternatively, one can also use IGMinimumVertexColoring[G]; it shows that three colors are already sufficient for this graph.

Alternatively, the style can also be applied with IGVertexMap:

Graph[G, GraphStyle -> "BasicBlack", VertexSize -> 1.5] //

  IGVertexMap[

    ColorData[97],

    VertexStyle -> IGMinimumVertexColoring

  ]

enter image description here

edited Dec 4 at 10:24

Szabolcs

158k13432926

answered Dec 3 at 23:37

Henrik Schumacher

47k466134

That's easy with Szabolcs' IGraph/M package:

Needs["IGraphM`"];

G = AdjacencyGraph[M];

colors = ColorData[97] /@ Range[4];

Graph[G,

 VertexStyle ->Thread[Range[VertexCount[G]] -> colors[[IGKVertexColoring[G, 4][[1]]]]

 ]

enter image description here

Alternatively, one can also use IGMinimumVertexColoring[G]; it shows that three colors are already sufficient for this graph.

Alternatively, the style can also be applied with IGVertexMap:

Graph[G, GraphStyle -> "BasicBlack", VertexSize -> 1.5] //

  IGVertexMap[

    ColorData[97],

    VertexStyle -> IGMinimumVertexColoring

  ]

enter image description here

edited Dec 4 at 10:24

Szabolcs

158k13432926

answered Dec 3 at 23:37

Henrik Schumacher

47k466134

edited Dec 4 at 10:24

Szabolcs

158k13432926

edited Dec 4 at 10:24

Szabolcs

158k13432926

edited Dec 4 at 10:24

Szabolcs

158k13432926

answered Dec 3 at 23:37

Henrik Schumacher

47k466134

answered Dec 3 at 23:37

Henrik Schumacher

47k466134

answered Dec 3 at 23:37

Henrik Schumacher

47k466134

I also need the list of nodes in each color. I prefer almost equal number of nodes in different colors.
– dipak narayanan
Dec 4 at 8:11

1

@dipaknarayanan Look up GroupBy: GroupBy[ Transpose[{VertexList[G], IGMinimumVertexColoring[G]}], Last -> First ]
– Szabolcs
Dec 4 at 9:28

add a comment |

I also need the list of nodes in each color. I prefer almost equal number of nodes in different colors.
– dipak narayanan
Dec 4 at 8:11

1

@dipaknarayanan Look up GroupBy: GroupBy[ Transpose[{VertexList[G], IGMinimumVertexColoring[G]}], Last -> First ]
– Szabolcs
Dec 4 at 9:28

I also need the list of nodes in each color. I prefer almost equal number of nodes in different colors.
– dipak narayanan
Dec 4 at 8:11

@dipaknarayanan Look up GroupBy: GroupBy[ Transpose[{VertexList[G], IGMinimumVertexColoring[G]}], Last -> First ]
– Szabolcs
Dec 4 at 9:28

add a comment |

up vote
5
down vote

You can also use the function MinimumVertexColoring from the Combinatorica package:

Needs["Combinatorica`"]

mvc = MinimumVertexColoring[FromAdjacencyMatrix@m];

colors = MapIndexed[#2[[1]] -> # &, ColorData[97] /@ mvc] ;

AdjacencyGraph[m, VertexSize -> 3/2, System`VertexStyle -> colors]

enter image description here

answered Dec 4 at 2:47

kglr

175k9197402

but I must have 4 colors and prefer almost equal number of nodes in different colors. And also the list of nodes in each color
– dipak narayanan
Dec 4 at 8:09

2

@dipak This "but" comes a bit late. Please, be explicit about your constraints the next time you ask a question. Hidden constraints are extremely frustrating for people who try to help you.
– Henrik Schumacher
Dec 4 at 9:08

1

@dipaknarayanan For that I suggest you research how to do graph colouring through integer programming and see if you want include your requirements as a constraint.
– Szabolcs
Dec 4 at 9:40

@kglr Are you still on M9? If you ever upgrade to 10.0+ and would like to contribute to IGraph/M, let me know. There is a lot that you could help with (it's not longer just an igraph interface). Unfortunately, IGraph/M won't work in the cloud version because of the C++ dependencies.
– Szabolcs
Dec 4 at 15:19

@Szabolcs, just upgraded to v11 a few weeks ago. I have installed IGraph/M and reading the documentation now. I would be happy to try my hand to help with what is needed.
– kglr
Dec 4 at 17:01

|
show 8 more comments

up vote
5
down vote

You can also use the function MinimumVertexColoring from the Combinatorica package:

Needs["Combinatorica`"]

mvc = MinimumVertexColoring[FromAdjacencyMatrix@m];

colors = MapIndexed[#2[[1]] -> # &, ColorData[97] /@ mvc] ;

AdjacencyGraph[m, VertexSize -> 3/2, System`VertexStyle -> colors]

enter image description here

answered Dec 4 at 2:47

kglr

175k9197402

but I must have 4 colors and prefer almost equal number of nodes in different colors. And also the list of nodes in each color
– dipak narayanan
Dec 4 at 8:09

2

@dipak This "but" comes a bit late. Please, be explicit about your constraints the next time you ask a question. Hidden constraints are extremely frustrating for people who try to help you.
– Henrik Schumacher
Dec 4 at 9:08

1

@dipaknarayanan For that I suggest you research how to do graph colouring through integer programming and see if you want include your requirements as a constraint.
– Szabolcs
Dec 4 at 9:40

@kglr Are you still on M9? If you ever upgrade to 10.0+ and would like to contribute to IGraph/M, let me know. There is a lot that you could help with (it's not longer just an igraph interface). Unfortunately, IGraph/M won't work in the cloud version because of the C++ dependencies.
– Szabolcs
Dec 4 at 15:19

@Szabolcs, just upgraded to v11 a few weeks ago. I have installed IGraph/M and reading the documentation now. I would be happy to try my hand to help with what is needed.
– kglr
Dec 4 at 17:01

|
show 8 more comments

up vote
5
down vote

You can also use the function MinimumVertexColoring from the Combinatorica package:

Needs["Combinatorica`"]

mvc = MinimumVertexColoring[FromAdjacencyMatrix@m];

colors = MapIndexed[#2[[1]] -> # &, ColorData[97] /@ mvc] ;

AdjacencyGraph[m, VertexSize -> 3/2, System`VertexStyle -> colors]

enter image description here

answered Dec 4 at 2:47

kglr

175k9197402

You can also use the function MinimumVertexColoring from the Combinatorica package:

Needs["Combinatorica`"]

mvc = MinimumVertexColoring[FromAdjacencyMatrix@m];

colors = MapIndexed[#2[[1]] -> # &, ColorData[97] /@ mvc] ;

AdjacencyGraph[m, VertexSize -> 3/2, System`VertexStyle -> colors]

enter image description here

answered Dec 4 at 2:47

kglr

175k9197402

answered Dec 4 at 2:47

kglr

175k9197402

answered Dec 4 at 2:47

kglr

175k9197402

answered Dec 4 at 2:47

kglr

175k9197402

but I must have 4 colors and prefer almost equal number of nodes in different colors. And also the list of nodes in each color
– dipak narayanan
Dec 4 at 8:09

2

@dipak This "but" comes a bit late. Please, be explicit about your constraints the next time you ask a question. Hidden constraints are extremely frustrating for people who try to help you.
– Henrik Schumacher
Dec 4 at 9:08

1

@dipaknarayanan For that I suggest you research how to do graph colouring through integer programming and see if you want include your requirements as a constraint.
– Szabolcs
Dec 4 at 9:40

@kglr Are you still on M9? If you ever upgrade to 10.0+ and would like to contribute to IGraph/M, let me know. There is a lot that you could help with (it's not longer just an igraph interface). Unfortunately, IGraph/M won't work in the cloud version because of the C++ dependencies.
– Szabolcs
Dec 4 at 15:19

@Szabolcs, just upgraded to v11 a few weeks ago. I have installed IGraph/M and reading the documentation now. I would be happy to try my hand to help with what is needed.
– kglr
Dec 4 at 17:01

|
show 8 more comments

but I must have 4 colors and prefer almost equal number of nodes in different colors. And also the list of nodes in each color
– dipak narayanan
Dec 4 at 8:09

2

@dipak This "but" comes a bit late. Please, be explicit about your constraints the next time you ask a question. Hidden constraints are extremely frustrating for people who try to help you.
– Henrik Schumacher
Dec 4 at 9:08

1

@dipaknarayanan For that I suggest you research how to do graph colouring through integer programming and see if you want include your requirements as a constraint.
– Szabolcs
Dec 4 at 9:40

@kglr Are you still on M9? If you ever upgrade to 10.0+ and would like to contribute to IGraph/M, let me know. There is a lot that you could help with (it's not longer just an igraph interface). Unfortunately, IGraph/M won't work in the cloud version because of the C++ dependencies.
– Szabolcs
Dec 4 at 15:19

@Szabolcs, just upgraded to v11 a few weeks ago. I have installed IGraph/M and reading the documentation now. I would be happy to try my hand to help with what is needed.
– kglr
Dec 4 at 17:01

but I must have 4 colors and prefer almost equal number of nodes in different colors. And also the list of nodes in each color
– dipak narayanan
Dec 4 at 8:09

@dipak This "but" comes a bit late. Please, be explicit about your constraints the next time you ask a question. Hidden constraints are extremely frustrating for people who try to help you.
– Henrik Schumacher
Dec 4 at 9:08

@dipaknarayanan For that I suggest you research how to do graph colouring through integer programming and see if you want include your requirements as a constraint.
– Szabolcs
Dec 4 at 9:40

@kglr Are you still on M9? If you ever upgrade to 10.0+ and would like to contribute to IGraph/M, let me know. There is a lot that you could help with (it's not longer just an igraph interface). Unfortunately, IGraph/M won't work in the cloud version because of the C++ dependencies.
– Szabolcs
Dec 4 at 15:19

@Szabolcs, just upgraded to v11 a few weeks ago. I have installed IGraph/M and reading the documentation now. I would be happy to try my hand to help with what is needed.
– kglr
Dec 4 at 17:01

|
show 8 more comments

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