Flows of physical quantities in large complex networks, natural or man made, rely in general on some scalar gradients existing in the networks. We investigate, analytically and numerically, under what conditions jamming in gradient flows can occur in random and scale-free networks. We find that the degree of jamming typically increases with the average connectivity $⟨k⟩$ of the network. A crossover phenomenon is uncovered where for $⟨k⟩<k_c$ ($k_c$ denotes a critical connectivity, estimated to be about 10), scale-free networks have a higher level of congestion than random networks with the same $⟨k⟩$, while the opposite occurs for $⟨k⟩>k_c$.

• Received 28 March 2005

DOI:https://doi.org/10.1103/PhysRevE.71.065105