Review article of various complexity measures of networks
Paul Anglin criticised our analysis of the neoclassical theory of the firm, but makes a number of incorrect assertions about our assumptions. We correct these misunderstandings, but acknowledge that one criticism he makes is correct. We correct this
flaw with a new argument that supersedes the flawed strategic reaction argument we presented in our previous paper.
Anthropic reasoning is a form of statistical reasoning based upon finding oneself a member of a particular reference class of conscious beings. By considering empirical distribution functions defined over animal life on Earth, we can deduce that the
vast bulk of animal life is unlikely to be conscious.
We have previously presented a critique of the standard Marshallian theory of the firm, and developed an alternative formulation that better agreed with the results of simulation. An incorrect mathematical fact was used in our previous presentation.
This paper deals with correcting the derivation of the Keen equilibrium, and generalising the result to the asymmetric case. As well, we discuss the notion of rationality employed, and how this plays out in a two player version of the game.
In previous work, I have developed an information theoretic complexity measure of networks. When applied to several real world food webs, there is a distinct difference in complexity between the real food web, and randomised control networks obtained
by shuffling the network links. One hypothesis is that this complexity surplus represents information captured by the evolutionary process that generated the network. In this paper, I test this idea by applying the same complexity measure to several well-known artificial life models that exhibit ecological networks: Tierra, EcoLab and Webworld. Contrary to what was found in real networks, the artificial life generated foodwebs had little information difference between itself and randomly shuffle
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 a
n 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. ...
The graph isomorphism problem is of practical importance, as well as being a theoretical curiosity in computational complexity theory in that it is not known whether it is $NP$-complete or $P$. However, for many graphs, the problem is tractable, and
related to the problem of finding the automorphism group of the graph. Perhaps the most well known state-of-the art implementation for finding the automorphism group is Nauty. However, Nauty is particularly susceptible to poor performance on star configurations, where the spokes of the star are isomorphic with each other. In this work, I present an algorithm that explodes these star configurations, reducing the problem to a sequence of simpler automorphism group calculations.
The term {em complexity} is used informally both as a quality and as a quantity. As a quality, complexity has something to do with our ability to understand a system or object -- we understand simple systems, but not complex ones. On another level, {
em complexity} is used as a quantity, when we talk about something being more complicated than another. In this chapter, we explore the formalisation of both meanings of complexity, which happened during the latter half of the twentieth century.
