## Traffic congestion: Tolls

In a preceding article we have used a simple model to demonstrate how selfish behavior can create additional congestion. One…

## Degrees in graphs I: the Handshake Lemma

A graph consists of objects called vertices and connections between them called edges. For every vertex, we can count how…

## Layered networks I: From manufacturing plants to queueing networks

Manufacturing plants convert raw material into a final product. Think of cars, where the production line consists of a large…

## Traffic congestion: Pigou's example

In network congestion models, we make some simplifying assumptions that make our life easier. In a large-scale system, each individual…

## Congested Roads

Traffic jams are one of the biggest inconveniences in modern time. They lead to stressful situations for commuters, and cause…

## The Erdös-Rényi random graph I

You could argue that random network theory started with one particular model, first studied by famous mathematicians Paul Erdös and…

## The Erdös-Rényi random graph II

A mathematical model of a network consists of elements and connections between them. We call the elements vertices, and the…

## The Erdös-Rényi random graph III

On the preceding pages we have introduced the Erdös-Rényi random graph model and posed the question when is it connected.…