Related papers: Network protocol scalability via a topological Kad…
Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…
We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the…
We derive the determinant of the Laplacian for the Hanoi networks and use it to determine their number of spanning trees (or graph complexity) asymptotically. While spanning trees generally proliferate with increasing average degree, the…
Nowadays, scaling methods for general large-scale complex networks have been developed. We proposed a new scaling scheme called "two-site scaling". This scheme was applied iteratively to various networks, and we observed how the degree…
Network topology is a flourishing interdisciplinary subject that is relevant for different disciplines including quantum gravity and brain research. The discrete topological objects that are investigated in network topology are simplicial…
Scale-free and non-computable characteristics of natural networks are found to result from the least-time dispersal of energy. To consider a network as a thermodynamic system is motivated since ultimately everything that exists can be…
Recent research has tried to extend the concept of renormalization, which is naturally defined for geometric objects, to more general networks with arbitrary topology. The current attempts do not naturally apply to directed networks, for…
I am showing how the ideas behind the renormalisation group can be generalised in order to produce the desired reduction in the degrees of freedom other that the ones considered up to now. Instead of looking only at the renormalisation…
It is shown in the framework of the N-component scalar model that the saddle point structure may generate non-trivial renormalization group flow. The spinodal phase separation can be described in this manner and a flat action is found as an…
Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second…
Many dynamical processes of complex systems can be understood as the dynamics of a group of nodes interacting on a given network structure. However, finding such interaction structure and node dynamics from time series of node behaviours is…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
A statistical ensemble of neural networks can be described in terms of a quantum field theory (NN-QFT correspondence). The infinite-width limit is mapped to a free field theory, while finite N corrections are mapped to interactions. After…
Despite their diverse origin, networks of large real-world systems reveal a number of common properties including small-world phenomena, scale-free degree distributions and modularity. Recently, network self-similarity as a natural outcome…
The Kadanoff-Wilson renormalization group approach for a scalar self-interacting field theor generally coupled with gravity is presented. An average potential that monitors the fluctuations of the blocked field in different scaling regimes…
We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…
We investigate structural transitions in adaptive networks where node states remain fixed and only the connections evolve via state-dependent rewiring. Using a general framework characterized by probabilistic rules for disconnection and…
Systems with lattice geometry can be renormalized exploiting their coordinates in metric space, which naturally define the coarse-grained nodes. By contrast, complex networks defy the usual techniques, due to their small-world character and…
Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph…
Preferential attachment is a central paradigm in the theory of complex networks. In this contribution we consider various generalizations of preferential attachment including for example node removal and edge rewiring. We demonstrate that…