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A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with…
A wavelet scattering network computes a translation invariant image representation, which is stable to deformations and preserves high frequency information for classification. It cascades wavelet transform convolutions with non-linear…
Given a complex network, its \emph{L-}paths correspond to sequences of $L+1$ distinct nodes connected through $L$ distinct edges. The \emph{L-}conditional expansion of a complex network can be obtained by connecting all its pairs of nodes…
The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the…
In this brief report, we present a disordered version of recursive networks. Depending on the structural parameters $u$ and $v$, the networks are either fractals with a finite fractal dimension $d_{f}$ or transfinite fractals (transfractal)…
For data represented by networks, the community structure of the underlying graph is of great interest. A classical clustering problem is to uncover the overall ``best'' partition of nodes in communities. Here, a more elaborate description…
Complex networks representing social interactions, brain activities, molecular structures have been studied widely to be able to understand and predict their characteristics as graphs. Models and algorithms for these networks are used in…
A number of network structural characteristics have recently been the subject of particularly intense research, including degree distributions, community structure, and various measures of vertex centrality, to mention only a few. Vertices…
The class of Koch fractals is one of the most interesting families of fractals, and the study of complex networks is a central issue in the scientific community. In this paper, inspired by the famous Koch fractals, we propose a mapping…
The spectral densities of the weighted Laplacian, random walk and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent $\beta$.…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…
Many real-world networks are embedded into a space or spacetime. The embedding space(time) constrains the properties of these real-world networks. We use the scale-dependent spectral dimension as a tool to probe whether real-world networks…
Although much of the focus of statistical works on networks has been on static networks, multiple networks are currently becoming more common among network data sets. Usually, a number of network data sets, which share some form of…
It is widely believed that fractality of complex networks origins from hub repulsion behaviors (anticorrelation or disassortativity), which means large degree nodes tend to connect with small degree nodes. This hypothesis was demonstrated…
Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
The fractal and self-similarity properties are revealed in many real complex networks. However, the classical information dimension of complex networks is not practical for real complex networks. In this paper, a new information dimension…
Fractals represent one of the fundamental manifestations of complexity, and fractal networks serve as tools for characterizing and investigating the fractal structures and properties of large-scale systems. Higher-order networks have…
Complex network theory has shown success in understanding the emergent and collective behavior of complex systems [1]. Many real-world complex systems were recently discovered to be more accurately modeled as multiplex networks [2-6]---in…