Friday, December 17, 2010

Networks: an introduction

I usually do not discuss here things closely related to my research area. This is for a number of reasons: for example, I usually write this blog in my spare time and I focus on different subjects. There are exceptions... for example I'm writing about PageRank (here, here and I have not yet finished), which is rather close to a specific part of what I'm doing (no, I'm not re-writing Google from scratch ;) ).

Nowadays I have lots of interest in network and graph theory. I like it because it keeps my maths fresh (I miss maths a lot, in fact) and most computer science and engineering subjects can be better grasped with a sound and complete (pun intended) understanding of graph theory.



I recently found a wonderful book, which is "Networks: An Introduction" by M.E.J. Newman. This is not about "computer networks" (though they are dealt with). It is about the maths behind networks. It is a single book which cover all the basis of network theory.

Different kinds of networks are described (biological, social, information). Network properties, metrics and measures are defined, and results on average properties for each kind of network are given, together with the large-scale description of such networks. Then, a whole lot of computer algorithms are presented. Models to generate networks (random graphs, Barabasi and Albert model, Strogatz and Watts model) are explained and eventually network processes (epidemics, percolation, node removal/addition, dynamic systems, search) are presented. Basically, it's all there.

Moreover, the book is very readable, even with little experience on the subject and each part is mostly independent. That is to say, it is possible to start reading almost from any point, which makes the book a great reference. But it is also a great introduction to the subject. And > 300 references mean that the book is a great hub to start further explorations of the world of networks.

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