Abstract 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 this paper, a complexity measure of networks is proposed based on the 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. I propose a simple representation language for undirected graphs that can be encoded as a bitstring, and equivalence is a topological equivalence. I also present an algorithm for computing the complexity of an arbitrary undirected network. 1 Introduction In [12], I argue that information content provides an overarching complexity measure that connects the many and various complexity measures proposed (see [6] for a review). The idea is fairly simple. In most cases, there is an obvious prefix-free representation language within which descriptions of the objects of interest can be encoded. There is also a classifier of descriptions that can determine if two descriptions correspond to the same object. This classifier is commonly called the observer, denoted O(x). To compute the complexity of some object x, count the number of equivalent descriptions!(`; x) = of length ` that map to the object x under the agreed classifier. Then the complexity of x is given in the limit as ` ! 1:

Abstract. ClassdescMP is a distributed memory parallel programming system for use with C++ and MPI. It uses the Classdesc reflection system to ease the task of building complicated messages to be sent between processes. It doesn’t hide the underlying MPI API, so it is an augmentation of MPI capabilities. Users can still call standard MPI function calls if needed for performance reasons. 1 Classdesc Reflection MPI is an application programming interface (API- in other words library of functions calls) for passing data from one unix process to another. The processes may be running on the same computer, or completely distinct computers, so this system provides a means of implementing distributed memory parallel processing. MPI has been used to great success in a variety of Engineering and Scientific codes where large arrays of the same type of data (eg floating point numbers) need to be exchanged between processes. However, with object oriented codes, one really needs to send objects (which may well be compound) between processes.

The concept of neutral evolutionary networks being a significant factor in evolutionary dynamics was first proposed by Huynen et al. about 7 years ago. In one sense, the principle is easy to state -- because most mutations to an organism are deleterious, one would expect that neutral mutations that don't affect the phenotype will have disproportionately greater representation amongst successor organisms than one would expect if each mutation was equally likely. So it was