Hidden Topological Structure of Flow Network Functionality

The ability to reroute and control flow is vital the function of venation networks across a wide range organisms. By modifying individual edges in these networks, either by adjusting edge conductances or creating destroying edges, organisms robustly propagation inputs perform specific tasks. However, fundamental disconnect exists between structure function: with different local architectures can same functions. Here, we answer question how changes at level collectively create functionality scale an entire network. Using persistent homology, analyze tuned complex We find that responses such encode hidden topological composed sectors nearly uniform pressure. Although are not apparent underlying network structure, they correlate strongly function. connectivity sectors, rather than nodes, provides quantitative relationship networks.