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# Tag Archives: er network

## The components of an ER network

ER networks have a strange property: even a small number of edges, distributed randomly, can lead to a connected structure with very high probability — the so-called “giant” component. Studying this effect brings up the notion of a critical threshold and a phase change, which can be calculated both mathematically and in simulation.

(This is a chapter from Complex networks, complex processes.)

## The mathematics of ER networks

Because Erdős-Rényi networks have a very simple and regular generation process, it’s reasonable to ask whether we can do better than numerical studies when trying to find its degree distribution, mean degree, and the like. And indeed we can.

(This is a chapter from Complex networks, complex processes.)

## Erdős-Rényi networks

Let’s leave epidemic spreading for a little while to return to the static structure of networks, and look at perhaps the most common class of network, the *Erdős-Rényi* or* ER network*. These networks are incredibly simple to describe, incredibly simple to build and simulate – and incredibly useful as at least first-attempt network models for a range of processes. We’ll also run up against the limitations of animation for presenting networks.

(This is a chapter from Complex networks, complex processes.)