Small-World Networks

I’ve been re-reading Sync: the emerging science of spontaneous order, by Steven Strogatz. Amongst other things he describes his work with Duncan Watts on ‘small-world networks’, supplying the mathematical rigour behind the ‘six degrees of separation‘ concept.

In modelling a network as an abstraction of nodes and linkages, they isolated two variables – average path length (AVP) and ‘clustering’. AVP measures the average ‘degrees of separation’ between two nodes, meaning how many other nodes they have to go through, on average, to reach any other node in the network. Clustering is the probability that two nodes linked to a common node will also be linked directly – that someone has two friends that are also friends of each other.

What they found is this – for a highly clustered network with very high AVP (a
bunch of tribes with only local contact), if just a few random links are introduced (between
members of distant tribes), AVP falls dramatically, while clustering remains very high. The
network becomes, in a sense, much more ‘efficient’, even though most members still think
they live in local clusters. This finding appears to have general application – nervous
systems, boards of directors, disease propagation, power grids and, of course, costars of
Kevin Bacon.

Attempts have already been made to examine these ideas in the context of corporate
organisational structures (basically, does introducing a few connections between ‘silos’
have a disproportionate effect on communication and coordination? I wonder whether
there might also be an optimising principle for activity maps – in formulating the
strategic architecture of a business or value network…

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