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I have a text file containing the adjacency matrix for my graph. Each value in the matrix corresponds to the edge weights between the respective vertex. How can I read this matrix using igraph package in python so that each edge is given its respective weight.

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since you seem to be a beginner, there is a python-igraph-tutorial.

You can also find the documentation there and for your specific problem you need the 'Read' method. You need to specify a file name and probably the adjacancy parameter.