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We consider the effects of network topology on the optimality of packet routing quantified by $gamma_c$, the rate of packet insertion beyond which congestion and queue growth occurs. The key result of this paper is to show that for any network, there exists an absolute upper bound, expressed in terms of vertex separators, for the scaling of $gamma_c$ with network size $N$, irrespective of the routing algorithm used. We then derive an estimate to this upper bound for scale-free networks, and introduce a novel static routing protocol which is superior to shortest path routing under intense packet insertion rates.
We investigate analytically and numerically the critical line in undirected random Boolean networks with arbitrary degree distributions, including scale-free topology of connections $P(k)sim k^{-gamma}$. We show that in infinite scale-free networks t
Scale-free networks with topology-dependent interactions are studied. It is shown that the universality classes of critical behavior, which conventionally depend only on topology, can also be explored by tuning the interactions. A mapping, $gamma = (
We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree distribution
Networks with a scale-free degree distribution are widely thought to promote cooperation in various games. Herein, by studying the well-known prisoners dilemma game, we demonstrate that this need not necessarily be true. For the very same degree sequ
A complete understanding of real networks requires us to understand the consequences of the uneven interaction strengths between a systems components. Here we use the minimum spanning tree (MST) to explore the effect of weight assignment and network