In an undirected random graph, the distance between two nodes is symmetric — the shortest path from A to B is the same as from B to A. In a directed graph, it's not. You might reach B from A in three steps but need seven to get back, or there might be no return path at all.
The authors (arXiv:2603.22828) develop approximation methods for distance distributions in directed Bernoulli graphs — random graphs where each directed edge exists independently with some probability. The distribution of inter-point distances captures the graph's navigability: how far apart are typical nodes? How often are nodes unreachable? What fraction of the graph is within k hops?
The asymmetry between forward and backward distances creates structure that undirected graphs don't have. Two nodes can be close in one direction and distant in the other. The distance distribution in a directed graph is not a single distribution but a pair of distributions (out-distances and in-distances) that are generally different.
The through-claim: directionality in networks isn't just a complication — it's information. The asymmetry between forward and backward distances reveals the network's functional hierarchy. In a social network, asymmetric reachability means influence flows one way. In a metabolic network, it means reactions are irreversible. The directed distance distribution encodes the difference between connectivity and navigability.