The Mathematics of Networks

March 13, 2004

Arriving in mathematical sciences departments by (snail) mail at about the same time as this issue of SIAM News will be the poster for Mathematics Awareness Month 2004.* The poster refers interested students---and their professors, friends, and relatives---to the Web site http://mathforum.org/mam/04, which offers a variety of short articles and links on this year's theme, The Mathematics of Networks.

Come April, we hope that readers will make use of these materials to explore the rich and active research area of networks. As made clear by the authors of several of the posted articles, this is an area in which the applications and the mathematics are advancing hand in hand. Many members of the SIAM community work in graph theory, which provides researchers investigating a variety of interesting networks---the Web and gene control networks being two examples---with solid and ever developing foundations for their work. The vertices and edges of graphs become nodes and links in the networks; as they do, physicists, biologists, sociologists, and economists are finding that their very different networks often have strikingly similar properties.

Readers will encounter familiar and not-so-familiar ideas---from connected component, graph diameter, node degree, and random graphs to small-world networks, scale-free networks, and power law distributions. We hope that many readers will be inspired to learn about this exciting area. Let SIAM News know if your explorations take an interesting turn!

*Sponsored by the Joint Policy Board for Mathematics (AMS, MAA, and SIAM).


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