Understanding the topology of complex systems abstracted to networks is important for unraveling their functional capabilities. Many such networks follow the small-world and scale-free regimes. Several models of artificially growing networks lead to this observed network topology. Most previously proposed models for growing networks, such as rich-get-richer and duplication-divergence, produce realistic network topologies but do not consider the effects of exogenous forces such as optimization for adaptation in shaping network topology. It is likely that such forces have shaped complex systems throughout their evolution. To develop further insights into possible mechanisms that shape networks, a model that uses several previously proposed network growth algorithms was developed to grow networks that adapt under exogenous stress. A decision tree problem was used to generate a complex Boolean function. Growing networks were required to adapt to correctly decode this function using an evolutionary selection process. Under this growth regimen all growing network models are similarly adaptable. The newly added nodes tend to cluster into pathways emanating from few inputs, regardless of the growth algorithm. Distribution of redundant pathways from inputs to the output follow a power-law function with a scaling exponent $(\sim 1.3)$. Similar distribution of redundant pathways was observed from inputs in a cell signaling network and an air traffic control network. A flat distribution of redundant pathways from inputs was observed in growing networks that do not attempt to adapt. This analysis provides initial insights into distribution of pathways in naturally evolving complex systems that have defined input-output relationships.

• Received 28 December 2005

DOI:https://doi.org/10.1103/PhysRevE.73.061912