Node Degree

up:: 040 MOC Complex Systems

Given a graph $G$ with Adjacency Matrix $A$, the degree of a node $i$ is given by

$$deg(i)={\text{sumlim}}_j{A}_{ij}$$

In the case of an undirected graph, since $A_{ij}=A_{ji}$, the order of the indices does not matter. For directed graphs, on the contrary, one has to distinguish between In Degrees and Out Degrees; then, much care is needed on the Adjacency Matrix index convention.

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References

• Casas, Alberto Aleta. “Networks, epidemics and collective behavior: from physics to data science”.