Network Density

up:: 041 MOC Graph Theory

Image from Sparse coding: A simple exploration | by Morgan | metaflow-ai.

Given a network with nodes and edges, we calculate its density (or connectance) as the fraction of all possible edges that it has.

That is,

For undirected Simple Graphs, we have that

by the definition of Average Degree.

Miscellaneous

A network’s density points to how “interconnected” it is. In particular, one says that a network is sparse if

and dense if it isn’t sparse.

This seems to point to a Second Brain’s “effectiveness”: The best Second Brains are always dense networks, since it’s best to add new information by connecting it to previous knowledge; conversely, networks that grow with isolated (or poorly connected) nodes tend to be sparse.

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References

• NEWMAN, Mark. Networks. Oxford university press, 2018.