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The New Science of Networks

Perseus Books, 2002

15 min read

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Networks everywhere follow the same simple mathematical laws – which matter to you more than you may think.

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Networks all have a meaningful similarity. Whether the network at hand is a party, a cell's molecular reaction, or the puzzling old bridges of Königsberg, Prussia, you could describe each one by using a branch of mathematics called “graph theory,” invented by Leonhard Euler in 1736. His long-dormant concept bloomed in the 1990s with the advent of the Internet and continues to yield insights into many important problems. Sounds a bit dry? Don't worry. Albert-László Barabási writes in a lively style (there's nary an equation in sight) with fun, informative anecdotes. The tale of how he and other scientists discovered "the laws of networks" unfolds like a detective story. After reading this book, you'll see networks everywhere and gain deeper insight into disparate phenomena, from biological systems to business organizations to the economics of "increasing returns." getAbstract recommends this clear, accessible book to anyone who has ever wondered about the ubiquitous webs that encompass all things. This is popular science at its best.

Summary

Connecting the Dots

Until 1875, the branches of the Pregel River split the city of Königsberg, Prussia, into four pieces. Seven bridges connected the pieces: Five crossed to an island in the middle of the river and two crossed branches of the river. These bridges gave rise to the following puzzle: "Could one walk across all seven bridges of Königsberg without crossing the same one twice?" No one could solve this puzzle, not even the brilliant Swiss-born mathematician Leonhard Euler. But in 1736, while trying to solve it, Euler discovered why people had been working on the problem for so long: The Königsberg Bridge puzzle was not solvable. With this proof of insolubility, Euler created a new branch of mathematics called “graph theory.”

A graph is a simple diagram resembling a child's connect-the-dots game. Euler reduced the Königsberg Bridge problem to dots and lines or, in the jargon of graph theory, nodes and links. He represented the four landmasses as nodes, drawing a dot for each. He represented the bridges as lines linking the dots. On paper, the graph of the Königsberg Bridge problem looks nothing like a Prussian city on a river. Rather, it looks a bit like a...

About the Author

Albert-László Barabási is the Emil T. Hofman professor of physics at the University of Notre Dame in Indiana. Science, The New York Times and other popular media have covered his work.

Albert-László Barabási

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The New Science of Networks

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Connecting the Dots

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