A novel approach to characterize branching network: Application to termite tunnel patterns

We defined a novel “branch length similarity” (BLS) entropy, S, on a simple network consisting of a single node and branches. This simple network is referred to as “unit branching network” (UBN) because UBNs are components of larger networks. As an application of BLS entropy, we considered the characterization of termite tunnel patterns because termite tunnel patterns can be broken down into a collection of simple units consisting of a single node and branches. These simple units correspond to UBNs. To this end, in additional to the entropy, we introduced the standard deviation (σ) of the difference in S between UBNs connected by a single tunnel branch. Forty simulated tunnel patterns were created for each of two termite species, Reticulitermes flavipes (Kollar) and Coptotermes formosanus Shiraki. These patterns were projected into -σ phase space in order to assess their topological properties. This approach showed that for R. flavipes, their coordinates were relatively more clustered than those of C. formosanus. This result reflected that these two species were differently constrained by emergent property resulting from simple worker's tunneling behavior. We believe that the approach proposed in this study can be a useful tool to explore termite tunnel systems, but not limited to termite system.