Abstract
We study shortest paths and spanning trees of complex networks with random edge weights. Edges which do not belong to the spanning tree are inactive in a transport process within the network. The introduction of quenched disorder modifies the spanning tree such that some edges are activated and the network diameter is increased. With analytic random-walk mappings and numerical analysis, we find that the spanning tree is unstable to the introduction of disorder and displays a phase-transitionlike behavior at zero disorder strength In the infinite network-size limit we obtain a continuous transition with the density of activated edges growing like and with the diameter-expansion coefficient growing like in the regular network, and first-order transitions with discontinuous jumps in and at for the small-world (SW) network and the Barabási-Albert scale-free (SF) network. The asymptotic scaling behavior sets in when where the crossover size scales as for the regular network, for the SW network, and for the SF network. In a transient regime with there is an infinite-order transition with for the SW network and for the SF network. It shows that the transport pattern is practically most stable in the SF network.
- Received 22 August 2002
DOI:https://doi.org/10.1103/PhysRevE.66.066127
©2002 American Physical Society