Learning about Network Theory

[kurtosis]

A very nice introduction - There is a also a lot of interesting material on these topics in the academic literature. Here's a couple of nice examples:

(1) M. Newman's publications contain a wealth of ideas and insights into these topics:

http://www-personal.umich.edu/~mejn/pubs.html

Also, much credit goes to Barabasi who made many contributions to this field and did much to popularize it (along with Watts and Strogatz)

http://www.barabasilab.com/pubs-revart.php

For the future, there are many interesting possibilities in the study of dynamical processes on networks (e.g. reaction-diffusion / message passing / synchronization) - for a high level treatment see this excellent review:

Critical phenomena in Complex Networks http://arxiv.org/abs/0705.0010

[bootload]

"... Also, much credit goes to Barabasi who made many contributions to this field and did much to popularize it (along with Watts and Strogatz) ..."

Watts & Stogatz are instrumental in our understanding of "small world networks" ~ http://en.wikipedia.org/wiki/Small-world_network and Barabasi discovered Hubs (frequency of connections between nodes) ~ http://en.wikipedia.org/wiki/Albert-Laszlo_Barabasi

"... error tolerance is not shared by all redundant systems: it is displayed only by a class of in-homogeneously wired called scale-free networks, which include the World-Wide Web, the Internet6, social networks7 and cells8. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by un-realistically high failure rates. However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks ..."

Barabasi is important because of this paper, Albert R., Jeong R., Barabasi A, "2000, Nature #406, pp 378-402., 'Error and attack tolerance of complex networks'", (pdf 249Kb) ~ http://www.barabasilab.com/pubs/CCNR-ALB_Publications/200007...

Do not forget Vespignani ~ http://en.wikipedia.org/wiki/Alessandro_Vespignani who applied both the small world network idea and hubs to produce network diagrams showing "spatial spreading of disease" ~ http://www.pnas.org/content/106/51/21484.full

[merraksh]

A good understanding of Graph Theory would help too. The books "Graphs and Hypergraphs" by Claude Berge and "Random Graphs" by Bela Bollobás are among the most important in the area.

[emehrkay]

Nice. I just got turned on to Neo4j.org (graph db) and the resources listed here will help me better understand what is going on.

[tjmaxal]

It goes to show you how complex the subject is when the intro is this long and requires this much explanation.

[mentatseb]

Btw, you can easily analyze your Facebook friend network:

http://blog.sociomantic.com/2010/05/using-netvizz-gephi-to-a...

Gephi is used to visualize graphs:

http://gephi.org/

[reader5000]

the bespectacled aristocrat in the photo is what sells it