Allometric scaling of von Neumann entropy in animal connectomes and its evolutionary aspect

The ubiquitous scaling relationships may serve as an entry point in understanding the structurofunctional complexities of animal connectomes. One of the possible approaches of framing such a relationship is based on the network’s community structure, where the scaling relation of a complexity measure with the respective community size is investigated. In recent times, the von Neumann entropy, a spectral complexity measure of networks, has found several applications in complex network analysis. In this article, we demonstrate the community-wise scaling attribute of the network von Neumann entropy for six different animal connectomes (p<0.0001, and R2>0.95). The community structures were determined by the well-known modularity maximization technique and subsequently optimized upon tuning the structural resolution parameter that allows the community detection at multiple scales. Interestingly, the allometric scaling exponents were noted to be monotonic with the phylogenetic order of the investigated species.