Related papers: Mesoscopics and fluctuations in networks
The Macroscopic Fluctuating Theory is presented from a practical and self consistent point of view. We take as starting point the assumption that a system at a mesoscopic scale is described by a field $\phi(x,t)$ that evolves by a Langevin…
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…
This paper presents a comprehensive analysis of the degree statistics in models for growing networks where new nodes enter one at a time and attach to one earlier node according to a stochastic rule. The models with uniform attachment,…
We propose a model of random diffusion to investigate flow fluctuations in complex networks. We derive an analytical law showing that the dependence of fluctuations with the mean traffic in a network is ruled by the delicate interplay of…
We study aggregation as a mechanism for the creation of complex networks. In this evolution process vertices merge together, which increases the number of highly connected hubs. We study a range of complex network architectures produced by…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…
We prove that the fluctuations of mesocopic linear statistics for orthogonal polynomial ensembles are universal in the sense that two measures with asymptotic recurrence coefficients have the same asymptotic mesoscopic fluctuations (under…
Nonextensive aspects of the degree distribution in Watts-Strogatz (WS) small-world networks, $P_{SW}(k)$, have been discussed in terms of a generalized Gaussian (referred to as {\it $Q$-Gaussian}) which is derived by the three approaches:…
We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree…
In this article an upscaled model is presented, for complex networks with highly clustered regions exchanging some abstract quantities in both, microscale and macroscale level. Such an intricate system is approximated by a partitioned open…
A network is a typical expressive form of representing complex systems in terms of vertices and links, in which the pattern of interactions amongst components of the network is intricate. The network can be static that does not change over…
Mixing patterns in large self-organizing networks, such as the Internet, the World Wide Web, social and biological networks are often characterized by degree-degree {dependencies} between neighbouring nodes. One of the problems with the…
We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of…
We present a theory that accurately describes the counting of excited states of a noninteracting fermionic gas. At high excitation energies the results reproduce Bethe's theory. At low energies oscillatory corrections to the many--body…
We establish the Strong Poisson Hypothesis for symmetric closed networks. In particular, the asymptotic independence of the nodes -- as the size of the system tends to infinity -- is proved.
We investigate the number fluctuations of spatially split many-boson systems employing a theorem about the maximally and minimally attainable variances of an observable. The number fluctuations of many-boson systems are given for different…
We show that any sequence $(x_n)_{n \in \mathbb{N}} \subseteq [0,1]$ that has Poissonian correlations of $k$-th order is uniformly distributed, also providing a quantitative description of this phenomenon. Additionally, we extend…
One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of…
The social networks that infectious diseases spread along are typically clustered. Because of the close relation between percolation and epidemic spread, the behavior of percolation in such networks gives insight into infectious disease…