Related papers: Self-affine Fractals Embedded in Spectra of Comple…
One of the hallmarks of real networks is their ability to perform increasingly complex tasks as their topology evolves. To explain this, it has been observed that as a network grows certain subsets of the network begin to specialize the…
Self-similarity is a property of fractal structures, a concept introduced by Mandelbrot and one of the fundamental mathematical results of the 20th century. The importance of fractal geometry stems from the fact that these structures were…
We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…
Complex networks are characterized by heterogeneous distributions of the degree of nodes, which produce a large diversification of the roles of the nodes within the network. Several centrality measures have been introduced to rank nodes…
The multifractal detrended fluctuation analysis of time series is able to reveal the presence of long-range correlations and, at the same time, to characterize the self-similarity of the series. The rich information derivable from the…
Many real-world complex networks actually have a bipartite nature: their nodes may be separated into two classes, the links being between nodes of different classes only. Despite this, and despite the fact that many ad-hoc tools have been…
Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…
Most networks of interest do not live in isolation. Instead they form components of larger systems in which multiple networks with distinct topologies coexist and where elements distributed amongst different networks may interact directly.…
A new method called diffusion factorial moment (DFM) is used to obtain scaling features embedded in spectra of complex networks. For an Erdos-Renyi network with connecting probability $p_{ER} < \frac{1}{N}$, the scaling parameter is $\delta…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four…
We explain that spectral networks are a unifying framework that incorporates both shear (Fock-Goncharov) and length-twist (Fenchel-Nielsen) coordinate systems on moduli spaces of flat SL(2,C) connections, in the following sense. Given a…
We introduce a new class of networks that grow by enhanced redirection. Nodes are introduced sequentially, and each either attaches to a randomly chosen target node with probability 1-r or to the ancestor of the target with probability r,…
It is well-known that randomly initialized, push-forward, fully-connected neural networks weakly converge to isotropic Gaussian processes, in the limit where the width of all layers goes to infinity. In this paper, we propose to use the…
It is well-known that fractal signals appear in many fields of science. LAN and WWW traces, wireless traffic, VBR resources, etc. are among the ones with this behavior in computer networks traffic flows. An important question in these…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
Fractal behavior and long-range dependence are widely observed in measurements and characterization of traffic flow in high-speed computer networks of different technologies and coverage levels. This paper presents the results obtained when…
Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…
The spectral dimension has been widely used to understand transport properties on regular and fractal lattices. Nevertheless, it has been little studied for complex networks such as scale-free and small world networks. Here we study the…
The spectrum of network is an important tool to study the function and dynamic properties of network, and graph operation and product is an effective mechanism to construct a specific local and global topological structure. In this study, a…