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Extracting Meaning From the Structure of Networks
Roland Piquepaille writes "Networks are used to represent the structure of complex systems, including the Internet or social networks, but often these descriptions are biased or incomplete. Now, researchers at the Santa Fe Institute (SFI) have shown that it's possible to extract automatically the hierarchical structure of networks. The researchers say their results 'suggest that hierarchy is a central organizing principle of complex networks, capable of offering insight into many network phenomena.' They also think that their algorithms can be applied to almost every kind of networks, from biochemical networks (protein interaction networks, metabolic networks or genetic regulatory networks) to communities in social networks. But read more for additional references and some pictures about hierarchical networks and their applications."
As is typical of a Roland the Plogger article, there's no link to the original article, but there's a link to his ad-laden blog. Here's the abstract:
Hierarchical structure and the prediction of missing links in networks
Nature 453, 98 (2008). doi:10.1038/nature06830
Authors: Aaron Clauset, Cristopher Moore & M. E. J. Newman
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, in which vertices divide into groups that further subdivide into groups of groups, and so forth over multiple scales. In many cases the groups are found to correspond to known functional units, such as ecological niches in food webs, modules in biochemical networks (protein interaction networks, metabolic networks or genetic regulatory networks) or communities in social networks. Here we present a general technique for inferring hierarchical structure from network data and show that the existence of hierarchy can simultaneously explain and quantitatively reproduce many commonly observed topological properties of networks, such as right-skewed degree distributions, high clustering coefficients and short path lengths. We further show that knowledge of hierarchical structure can be used to predict missing connections in partly known networks with high accuracy, and for more general network structures than competing techniques. Taken together, our results suggest that hierarchy is a central organizing principle of complex networks, capable of offering insight into many network phenomena.
So now, unlike Roland, we now have a clue what's being talked about. It's a scheme for finding some structure in networks and inferring what links might be missing.
I was about to take offence at that statement, but then I realized I'm not Roland Pipe.. pip.. something.
But I had to laugh at the title. The meaning of the structure of networks is a stupid idea. The purpose maybe, the philosophy behind the structure maybe. But the meaning of? Go ask a Dadaist.
Do it yourself, because no one else will do it yourself. [beta blockade 10-17 Feb]
In the context of the research (using known parts of a network's structure to predict unknown parts), I don't think the word "meaning" is out of place at all. A hierarchical clustering algorithm will extract some kind of hierarchy from any network you throw at it - but does that hierarchy mean anything? Does it contain information? This new research suggests that, for certain kinds of network, the extracted hierarchy is meaningful, because it allows us to make predictions about unknown parts of the network that we could not make without first extracting the hierarchy.
That's actually quite a profound discovery, because in the last ten years, complex networks (especially small-world and scale-free networks) have been held up as models of natural decentralisation and non-hierarchical self-organisation in many fields, from ecology to politics to communications to epidemiology. If such networks turn out to contain meaningful hierarchies (i.e. hierarchies that actually tell us something about how they function) then much of the rhetoric about complex systems will be turned on its head.