Directionality of real world networks as predicted by path length in directed and undirected graphs

• We propose a novel score to detect whether networks have an inherent order.
• We show that real world networks contain an inherent order.
• The same score helps ordering the nodes in such a network.
• When applied to neural networks, the classification into sensory and motor neurons emerges directly from this order.

Many real world networks either support ordered processes, or are actually representations of such processes. However, the same networks contain large strong connectivity components and long circles, which hide a possible inherent order, since each vertex can be reached from each vertex in a directed path. Thus, the presence of an inherent directionality in networks may be hidden. We here discuss a possible definition of such a directionality and propose a method to detect it.Several common algorithms, such as the betweenness centrality or the degree, measure various aspects of centrality in networks. However, they do not address directly the issue of inherent directionality. The goal of the algorithm discussed here is the detection of global directionality in directed networks. Such an algorithm is essential to detangle complex networks into ordered process.We show that indeed the vast majority of measured real world networks have a clear directionality. Moreover, this directionality can be used to classify vertices in these networks from sources to sinks. Such an algorithm can be highly useful in order to extract a meaning from large interaction networks assembled in many domains.