Static Network Structure Affects the Dynamics of Emergent Landscapes version 2010-02-26 Emergence: The Relation between Static Network Structure and the Dynamic Qualities of Landscapes

In a network individual nodes can have differing numbers of links. Barabási (2003), among others, proposes that self-organizing networks in nature are scale-free, yielding many nodes with few connections and few nodes with many connections; the (log-log) frequency of connections per node should follow a power law. In contrast, random graphs should produce non-power-law connections-per-node distributions. Our NK Boolean simulation program, E42, generated networks whose nodes came into existence Simultaneously or in a developmental Order. In Simultaneous networks, all N nodes simultaneously connect their K links randomly among all nodes; in Ordered networks each node receives links only from nodes that are created after it; thus nodes that exist earlier have more opportunity to get links from later nodes. The .95 confidence interval for mean log-log regression slopes for 1000 Simultaneous networks was -1.046 > -1.031 < -1.017 and -1.442 > -1.428 < -1.414 for 1000 Ordered networks. Thus Ordered networks do have a scale-free, fractal structure whereas Simultaneous networks do not. Static network structure is one thing; the dynamics of what flows across a network is another. Our research focus is on finding the relationship between static network structure and the dynamics of the flow across the networks. We frame dynamic flow in terms of the landscape theory. In samples of 50 networks per type we found that Ordered networks produce landscapes that are more rugged but are more homogeneous and more susceptible to taxonomic