Accessibility in networks: A useful measure for understanding social insect nest architecture

Networks and the associated tools from graph theory have now become well-established approaches to study natural as well as human-made systems. While early studies focused on topology and connectivity, the recent literature has acknowledged the importance of the dynamical properties of these networks. Here we focus on such a dynamic measure: accessibility. It characterizes for any given movement dynamics (such as random walks) the average number of nodes that can be reached in exactly h steps (out-accessibility), or the average number of nodes from which a given node can be reached (in-accessibility). This focus on dynamics makes accessibility particularly appropriate to study movement on networks and to detect complementary properties with respect to topology-based measurements such as betweenness centrality. We apply this measure to six nests of Cubitermes termites. Their mushroom-like 3D architectures consist of chambers and connecting tunnels that can be associated to nodes and edges in a communication network. Accessibilities turn out to be particularly low in the bottom part of the nests that link them to their underground tunneling network. We interpret this result in the context of anti-predator (ants) behavior and/or as a side effect of the global nest shape.