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The Mysterious R explained in simple terms

During the Corona pandemic the reproduction number R appeared in much of the media. While it is not at all obvious what this quantity measures exactly, it is obvious that making it smaller than 1 really is crucial in controlling the spread of the virus. So what is this R really?

How the popular become even more popular

Many networks, from technological to social networks, and from the world-wide web to collaboration networks, have a hub-like structure. Why is this the case, and why are they not much more homogeneous?

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 many neighbors it has, which is called its degree.

Small worlds and six degrees of separation

Social networks are remarkably small, in the sense that you can hop between any two individuals in them using only a few hops. This video explains what such small-world networks are, why social networks are so small.

Influence in complex networks

Friends influence each other in their opinion of many aspects of life. In this video we describe how the level of connectedness in a social network relates to the extent in which individuals in it influence each other.