Mechanical generation of networks with surplus complexity

In previous work I examined an information based complexity measure of networks with weighted links. The measure was compared with that obtained from by randomly shuffling the original network, forming an Erdos-Renyi random network preserving the original link weight distribution. It was found that real world networks almost invariably had higher complexity than their shuffled counterparts, whereas networks mechanically generated via preferential attachment did not. The same experiment was performed on foodwebs generated by an artificial life system, Tierra, and a couple of evolutionary ecology systems, EcoLab and WebWorld. These latter systems often exhibited the same complexity excess shown by real world networks, suggesting that the complexity surplus indicates the presence of evolutionary dynamics. In this paper, I report on a mechanical network generation system that does produce this complexity surplus. The heart of the idea is to construct the network of state transitions of a chaotic dynamical system, such as the Lorenz equation. This indicates that complexity surplus is a more fundamental trait than that of being an evolutionary system.Comment: Accepted for ACALCI 2015 Newcastle, Australi

Complexity of Networks (reprise)

Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as species enter an ecosystem via migration or speciation, and leave via extinction. In a previous paper, a complexity measure of networks was proposed based on the {\em complexity is information content} paradigm. To apply this paradigm to any object, one must fix two things: a representation language, in which strings of symbols from some alphabet describe, or stand for the objects being considered; and a means of determining when two such descriptions refer to the same object. With these two things set, the information content of an object can be computed in principle from the number of equivalent descriptions describing a particular object. The previously proposed representation language had the deficiency that the fully connected and empty networks were the most complex for a given number of nodes. A variation of this measure, called zcomplexity, applied a compression algorithm to the resulting bitstring representation, to solve this problem. Unfortunately, zcomplexity proved too computationally expensive to be practical. In this paper, I propose a new representation language that encodes the number of links along with the number of nodes and a representation of the linklist. This, like zcomplexity, exhibits minimal complexity for fully connected and empty networks, but is as tractable as the original measure. ...Comment: Accepted in Complexit