Determining function from structure in neural networks

Previous work has investigated evolutionary trends in an information-theoretic measure of neural complexity, and related those trends to behavioral adaptation to the environment. This ("TSE") complexity measure thus appears to quantify the dynamical function of neural networks in an evolutionarily meaningful way. Other work has demonstrated that trends in increasing complexity are accompanied by corresponding trends toward increased clustering coefficient and decreased average minimum path length in the graphs that describe the underlying neural architectures. These results suggest an evolutionary trend towards so-called "small world" networks, and a correlation between small-world-ness and complexity. After a review of these results, I will ask the question: What other graph-theoretic metrics can we examine to further illuminate the relationship between network structure and network function, and what might they tell us about biological brains?