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We introduce new clustering coefficients for weighted networks. They are continuous and robust against edge weight changes. Recently, generalized clustering coefficients for weighted and directed networks have been proposed. These…

Networks are topological and geometric structures used to describe systems as different as the Internet, the brain or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying…

We propose and study a model of weighted scale-free networks incorporating a stochastic scheme for weight assignments to the links, taking into account both the popularity and fitness of a node. As the network grows the weights of links are…

Complex network reconstruction is a hot topic in many fields. Currently, the most popular data-driven reconstruction framework is based on lasso. However, it is found that, in the presence of noise, lasso loses efficiency for weighted…

In this article we prove a Generalized Asypmtotic Equipartition Property for Networked Data Structures modelled as coloured random graphs. The main techniques in this article remains large deviation principles for suitably defined empirical…

We study the problem of modeling multiple symmetric, weighted networks defined on a common set of nodes, where networks arise from different groups or conditions. We propose a model in which each network is expressed as the sum of a shared…

We will introduce two evolving models that characterize weighted complex networks. Though the microscopic dynamics are different, these models are found to bear a similar mathematical framework, and hence exhibit some common behaviors, for…

Networks describe a range of social, biological and technical phenomena. An important property of a network is its degree correlation or assortativity, describing how nodes in the network associate based on their number of connections.…

Understanding the mathematical properties of graphs underling biological systems could give hints on the evolutionary mechanisms behind these structures. In this article we perform a complete statistical analysis over thousands of graphs…

Finding the common structural brain connectivity network for a given population is an open problem, crucial for current neuro-science. Recent evidence suggests there's a tightly connected network shared between humans. Obtaining this…

In recent years, graph-based machine learning techniques, such as reinforcement learning and graph neural networks, have garnered significant attention. While some recent studies have started to explore the relationship between the graph…

Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing…

The geometric renormalization technique for complex networks has successfully revealed the multiscale self-similarity of real network topologies and can be applied to generate replicas at different length scales. In this letter, we extend…

In most networks, the connection between a pair of nodes is the result of their mutual affinity and attachment. In this letter, we will propose a Mutual Attraction Model to characterize weighted evolving networks. By introducing the initial…

Load balancing between adjacent base stations (BSs) is important for balancing load distributions and improving service provisioning. Whilst load balancing between any given pair of BSs is beneficial, cascade load sharing can cause network…

Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the…

While the vast majority of the literature on models for temporal networks focuses on binary graphs, often one can associate a weight to each link. In such cases the data are better described by a weighted, or valued, network. An important…

One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of…

This paper considers generalised network, intended as networks where (a) the edges connecting the nodes are nonlinear, and (b) stochastic processes are continuously indexed over both vertices and edges. Such topological structures are…