Network science [Guest Editorial

Abstract

Network science is relatively new, but its roots go all the way back to Leonhard Euler and the Bridges of Königsberg problem of 1735. Euler showed that it was impossible to parade through town crossing each of its seven bridges only once without repeating a crossing, and established a new field of mathematical research called graph theory [1]. Graph theory remained the providence of mathematicians for 200 years until sociologist Stanley Milgram used it to explain social networks called small worlds. Milgram’s experiment startled the world by showing, experimentally, that any two people in the United States are separated by a relatively small number of intermediaries. His experiment established the now-famous “six degrees of separation” and stimulated renewed interest in application of graph theory to real problems. Then in the 1990s a small group of physicists became interested in graph theory as it pertained to Ising, percolation theory, and phase transition. Their contribution became known as the “new science of networks,” and emphasized topological structure rather than graph algorithms. Their work attempted to justify the age-old paradigm “function follows form.”