Mathematics for Graphs
Familiarize yourself with two major elements of graphs: graph Laplacian and eigenvalues.
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The basic maths for processing graph-structured data
We already defined the graph signal and the adjacency matrix . 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 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 . 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 matrix:
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