Related papers: Non-linear growth and condensation in multiplex ne…

We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…

While actors in a population can interact with anyone else freely, social relations significantly influence our inclination towards particular individuals. The consequence of such interactions, however, may also form the intensity of our…

In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…

We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arises under various centrality measures, and…

We introduce a framework to intertwine dynamical processes of different nature, each with its own distinct network topology, using a multilayer network approach. As an example of collective phenomena emerging from the interactions of…

For most networks, the connection between two nodes is the result of their mutual affinity and attachment. In this paper, we propose a mutual selection model to characterize the weighted networks. By introducing a general mechanism of…

Convolutional Neural Networks (CNNs) have been widely applied. But as the CNNs grow, the number of arithmetic operations and memory footprint also increase. Furthermore, typical non-linear activation functions do not allow associativity of…

We propose a model for evolving networks by merging building blocks represented as complete graphs, reminiscent of modules in biological system or communities in sociology. The model shows power-law degree distributions, power-law…

In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…

Can multilayer neural networks -- typically constructed as highly complex structures with many nonlinearly activated neurons across layers -- behave in a non-trivial way that yet simplifies away a major part of their complexities? In this…

Mechanistic models can provide an intuitive and interpretable explanation of network growth by specifying a set of generative rules. These rules can be defined by domain knowledge about real-world mechanisms governing network growth or may…

We propose a model of network growth in which the network is co-evolving together with the dynamics of a quantum mechanical system, namely a quantum walk taking place over the network. The model naturally generalizes the Barab\'{a}si-Albert…

In multiplex networks, cycles cannot be characterized only by their length, as edges may occur in different layers in different combinations. We define a classification of cycles by the number of edges in each layer and the number of…

Learning latent structure in complex networks has become an important problem fueled by many types of networked data originating from practically all fields of science. In this paper, we propose a new non-parametric Bayesian…

Elements of networks interact in many ways, so modeling them with graphs requires multiple types of edges (or network layers). Here we show that such multiplex networks are generically more vulnerable to global cascades than simplex…

We prove almost sure convergence of the maximum degree in an evolving graph model combining a growing number of local choices with sublinear preferential attachment. At each step in the growth of the graph, a new vertex is introduced. Then…

The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the…

The coexistence of multiple types of interactions within social, technological and biological networks has moved the focus of the physics of complex systems towards a multiplex description of the interactions between their constituents.…

Multiplex networks are networks composed of multiple layers such that the number of nodes in all layers is the same and the adjacency matrices between the layers are diagonal. We consider the special class of multiplex networks where the…