## 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…

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

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

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

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

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

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

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