3 research outputs found
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