A molecular network rewiring rule that represents spatial constraint

Hideaki Suzuki
National Institute of Information and Communications Technol

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     Last modified: August 16, 2006

Abstract
Network artificial chemistry (NAC) is an approach to
emulating molecular interaction in a solvent with a
mathematical graph. To emulate molecules' spatial movement
in a 3D space, we have to appropriately design rewiring
rules for the NAC's weakest edges (van der Waals edges) so
that the edges imitate the contact relation between
molecules or atomic clusters. The paper presents one
candidate solution for this problem. First, an energy
function of network is introduced, and a rewiring rule is
formulated using the criterion of the minimization of the
energy. The energy consists of the node degree's diversity
term and the second shortest path term, and its
minimization makes a network have topological properties of
a regular graph. Second, we conduct a NAC simulation using
the established rewiring rule and compare the results with
those of a random walk simulation that emulates Brownian
motion of hard spheres in a 3D Euclid space. It is shown
that the two experimental results are in good agreement
with each other in terms of such network properties as the
cluster coefficient and average path length or the joining
and cutting probabilities of edges.

This is an invited paper in the session titled "Life and
Computation".