How small is a small-world network?

phys.org | 5/22/2018 | Staff
blackyblacky (Posted by) Level 3
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Discovered in the field of social sciences in the 1960s, the phenomenon known as small-world networks has fascinated popular culture and science for decades. It arose from the observation that in the world, any two people are connected by a short chain of social ties.

A network, whether natural (neural or social) or artificial (communication or transport systems) is an ordered set of elements connected to each other through various methods that share information. The small-world property is a property of networks in which, despite a large number of nodes, it is possible to find short communication paths between them. In recent decades it has been proved that both in natural and artificial systems, many real networks are also small-world. But, are all small-world networks small, and how do they compare to others?

World - Size - Objects - Reference - System

In the physical world we evaluate and compare the size of objects by contrasting them to a common reference, usually a standard metric system defined and agreed by the community. In the case of complex networks, the difference is that every network constitutes its own metric space. Thus, the question of whether a network is smaller or larger than another implies the comparison of two different spaces with each other, rather than the more familiar situation in which two objects are contrasted within the space they share.

Despite the existing variety of small-world networks, it still remains a challenge to make a reliable and comparable measurement of their average length.

Result - Study - Nature - Communications - Physics

The main result of a study published in Nature Communications Physics on 14 November is "the identification of the lower and upper boundaries for the average pathlength and global efficiency for (di)graphs of arbitrary number...
(Excerpt) Read more at: phys.org
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