The basic maths for processing graph-structured data

We already defined the graph signal XRN×FX \in R^{N \times F}and the adjacency matrix ARN×NA \in R^{N \times N}. A very important and practical feature is the degree of each node, which is simply the number of nodes that it is connected to. For instance, every non-corner pixel in an image has a degree of 8, which is the surrounding pixels.

If AA is binary, the degree corresponds to the number of neighbors in the graph. In general, we calculate the degree vector by summing the rows of AA. Since the degree corresponds to some kind of feature that is linked to the node, it is more convenient to place the degree vector in a diagonal N×NN \times N matrix:

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