Routes Obey Hierarchy in Complex Networks

Various hypotheses exist about the paths used for communication between the nodes of complex networks. Most studies simply suppose that communication goes via shortest paths, while others have more explicit assumptions about how routing (alternatively navigation or search) works or should work in real networks. However, these assumptions are rarely checked against real data. Here we directly analyze the structure of operational paths using real measurements. For this purpose we use existing and newly created datasets having both the topology of the network and a sufficient number of empirically-determined paths over it. Such datasets are processed for air transportation networks, the human brain, the Internet and the fit-fat-cat word ladder game. Our results suggest that from the great number of possible paths, nature seems to pick according to some simple rules, which we will refer to as routing policies. First we confirm, that the preference of short paths is an inevitable policy element, however the observed stretch of the paths suggests that there are other policies at work simultaneously. We identify two additional policies common in our networks: the "conform hierarchy", meaning that the paths should obey the structural hierarchy of the network, and the "prefer downstream" policy which promotes avoiding the network core if possible. Building upon these simple policies, we propose a synthetic routing policy which can recover the basic statistical properties of the operational paths in networks. Our results can be helpful in estimating the reaction of complex systems for stress coming from the outside more accurately than the shortest path assumption permits.