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Six degrees of separation: Why it is a small world after all

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A study conducted by the University of Leicester and KU Leuven, Belgium, examined how small worlds emerge spontaneously in all kinds of networks, including neuronal and social networks, giving rise to the well-known phenomenon of “Six degrees of separation”.

Many systems show complex structures, of which a distinctive feature is small-world network organization.

They arise in society as well as ecological and protein networks, the networks of the mammalian brain, and even human-built networks such as the Boston subway and the World Wide Web.

A study recently published in Scientific Reports by an international team of academics from the University of Leicester and KU Leuven showed that these remarkable structures are reached and maintained by the network diffusion, i.e. the traffic flow or information transfer occurring on the network.

Nicholas Jarman, who recently completed his PhD degree at the Department of Mathematics, and is first author of the study, said: “Algorithms that lead to small-world networks have been known in scientific community for many decades. The Watts-Strogatz algorithm is a good example. The Watts-Strogatz algorithm was never meant to address the problem of how small-world structure emerges through self-organisation. The algorithm just modifies a network that is already highly organised.”

Dr Ivan Tyukin from the University of Leicester added: “The fact that diffusion over network graph plays crucial role in keeping the system at a somewhat homeostatic equilibrium is particularly interesting. Here we were able to show that it is the diffusion process, however small or big gives rise to small-world network configurations that remain in this peculiar state over long intervals of time. At least as long as we were able to monitor the network development and continuous evolution”.

“Small-world networks, in which most nodes are not neighbours of one another, but most nodes can be reached from every other node by a small number of steps, were described in mathematics and discovered in nature and human society long ago, in the middle of the previous century. The question, how these networks are developing by nature and society remained not completely solved despite of many efforts applied during last twenty years. The work of N. Jarman with co-authors discovers a new and realistic mechanism of emergence of such networks. The answer to the old question became much clearer! I am glad that the University of Leicester is a part of this exciting research.”


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