# 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 $X \in R^{N \times F}$and the adjacency matrix $A \in R^{N \times N}$. 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 $A$ 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 $A$. 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 $N \times N$ matrix:

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