Local structure of directed networks.
Previous work on undirected small-world networks established the paradigm that locally structured networks tend to have a high density of short loops. On the other hand, many realistic networks are directed. Here we investigate the local organization of directed networks and find, surprisingly, that real networks often have very few short loops as compared to random models. We develop a theory and derive conditions for determining if a given network has more or less loops than its randomized counterparts. These findings carry broad implications for structural and dynamical processes sustained by directed networks.
Bianconi
Ginestra
G
The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy.
Gulbahce
Natali
N
Motter
Adilson E
AE
D000818:Animals; D017173:Caenorhabditis elegans / Q000033:anatomy & histology; D003195:Computer Communication Networks; D020387:Food Chain; D008962:Models, Theoretical; D009415:Nerve Net; D012441:Saccharomyces cerevisiae; D012944:Social Support