Related papers: Multiscale network renormalization: scale-invarian…
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…
This paper develops a framework for analyzing and designing dynamic networks comprising different classes of nodes that coexist and interact in one shared environment. We consider {\em ad hoc} (i.e., nodes can leave the network unannounced,…
Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…
Empirical studies show that real world networks often exhibit multiple scales of topological descriptions. However, it is still an open problem how to identify the intrinsic multiple scales of networks. In this article, we consider…
Complex networks are now being studied in a wide range of disciplines across science and technology. In this paper we propose a method by which one can probe the properties of experimentally obtained network data. Rather than just measuring…
We explore how minimal neural networks can invert the renormalization group (RG) coarse-graining procedure in the two-dimensional Ising model, effectively ``dreaming up'' microscopic configurations from coarse-grained states. This task -…
Different weighted scale-free networks show weights-topology correlations indicated by the non linear scaling of the node strength with node connectivity. In this paper we show that networks with and without weight-topology correlations can…
Representing various networked data as multiplex networks, networks of networks and other multilayer networks can reveal completely new types of structures in these system. We introduce a general and principled graphlet framework for…
Reconstructing a network of dynamic systems from observational data is an active area of research. Many approaches guarantee a consistent reconstruction under the relatively strong assumption that the network dynamics is governed by…
Real-world networks, e.g. the social relations or world-wide-web graphs, exhibit both small-world and scale-free behaviour. We interpret lattice triangulations as planar graphs by identifying triangulation vertices with graph nodes and…
We consider a class of simple, non-trivial models of evolving weighted scale-free networks. The network evolution in these models is determined by attachment of new vertices to ends of preferentially chosen weighted edges. Resulting…
The structure of many financial networks is protected by privacy and has to be inferred from aggregate observables. Here we consider one of the most successful network reconstruction methods, producing random graphs with desired link…
We investigate the searchability of complex systems in terms of their interconnectedness. Associating searchability with the number and size of branch points along the paths between the nodes, we find that scale-free networks are relatively…
In the paper, we present an incremental approach in the construction of scale free networks with hidden variables. The work arises from the necessity to generate that type of networks with a given number of links instead of obtaining a…
This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds…
We study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. We contend that the model displays a normal continuous phase transition with a…
Graph generation is one of the most challenging tasks in recent years, and its core is to learn the ground truth distribution hiding in the training data. However, training data may not be available due to security concerns or unaffordable…
Modeling complex spatial networks with multiscale heterogeneity poses significant mathematical and computational challenges. Lacking explicit PDE discretizations and facing excessive degrees of freedom, conventional methods often become…
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all…
Network embedding aims to learn the low-dimensional representations of vertexes in a network, while structure and inherent properties of the network is preserved. Existing network embedding works primarily focus on preserving the…