During the Corona pandemic the reproduction number 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 really?
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?
How are elements in real-world networks connected? That is the question we aim to answer in this post. Most real-world networks turn out to be extremely inhomogeneous.
Paul Erdős and Tibor Gallai developed a beautiful criterion to decide precisely when a degree sequence is graphical.
The degree sequence of a graph is the sequence of degrees of all its elements.
Written for the course `Random Graphs' at Eindhoven University of Technology, and class room tested for over ten years, the book `Random Graphs and Complex Networks' has now finally appeared in print at Cambridge University Press.
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.
The Networks Pages proudly presents the winner of the first Network Pages contest for the best logo, wordart image or artistic network photo: Stella Kapodistria.
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.
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.