In Degree

up:: Node Degree

(Image from Divergence and Curl « Diet Physics)

The in-degree of a node in a graph is the amount of arrows coming into it. It is a measure of how many arrows crash into a given node.

Using the Outward-Arrows Convention

$$A_{ij}\equiv A_{i\to j}$$

then the in-degree of a node $i$ is denoted as

$$de{g}^{-}(i)=\sum _j{A}_{ji}\equiv {\text{sumlim}}_j{A}_{j\to i}$$

Much care is due to this definition, as it relies entirely on the convention of the Adjacency Matrix $A$.

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References

• MATA, A. S. D. Complex Networks: a Mini-review. Brazilian Journal of Physics, v. 50, n. 5, p. 658–672, out. 2020.
• Directed graph - Wikipedia