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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, $gamma = (gamma - mu)/(1-mu)$, describes how a shift of the standard exponent $gamma$ of the degree distribution $P(q)$ can absorb the effect of degree-dependent pair interactions $J_{ij} propto (q_iq_j)^{-mu}$. Replica technique, cavity method and Monte Carlo simulation support the physical picture suggested by Landau theory for the critical exponents and by the Bethe-Peierls approximation for the critical temperature. The equivalence of topology and interaction holds for equilibrium and non-equilibrium systems, and is illustrated with interdisciplinary applications.
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
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
The studies based on $A+A rightarrow emptyset$ and $A+Brightarrow emptyset$ diffusion-annihilation processes have so far been studied on weighted uncorrelated scale-free networks and fractal scale-free networks. In the previous reports, it is widely
Networks with fat-tailed degree distributions are omnipresent across many scientific disciplines. Such systems are characterized by so-called hubs, specific nodes with high numbers of connections to other nodes. By this property, they are expected to
In the reaction-diffusion process $A+B to varnothing$ on random scale-free (SF) networks with the degree exponent $gamma$, the particle density decays with time in a power law with an exponent $alpha$ when initial densities of each species are the sa