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Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel…

We study the averaging-based distributed optimization solvers over random networks. We show a general result on the convergence of such schemes using weight-matrices that are row-stochastic almost surely and column-stochastic in expectation…

Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time…

Inspired by river networks and other structures formed by Laplacian growth, we use the Loewner equation to investigate the growth of a network of thin fingers in a diffusion field. We first review previous contributions to illustrate how…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

Following up on a previous work we examine a model of transportation network in some source-sink flow paradigm subjected to growth and resource allocation. The model is inspired from plants, and we add rules and factors that are analogous…

Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…

The apparent disconnection between the microscopic and the macroscopic is a major issue in the understanding of complex systems. To this extend, we study the convergence of repeatedly applying local rules on a network, and touch on the…

Inspired by the structure of technological networks, we discuss network evolution mechanisms which give rise to topological properties found in real spatial networks. Thus, the peculiar structure of transport and distribution networks is…

The advent of Internet and World Wide Web has led to unprecedent growth of the information available. People usually face the information overload by following a limited number of sources which best fit their interests. It has thus become…

The paper investigates the throughput behavior of single-commodity dynamical flow networks governed by monotone distributed routing policies. The networks are modeled as systems of ODEs based on mass conversation laws on directed graphs…

This work is concerned with the intricate interplay between node or pore pressures and connection or throat conductivities in flow or pore networks. A setting similar to pore networks is given by fracture networks. Recently, a non-local…

Adaptive networks are suitable for decentralized inference tasks, e.g., to monitor complex natural phenomena. Recent research works have intensively studied distributed optimization problems in the case where the nodes have to estimate a…

This paper proposes a supervised training algorithm for learning stochastic resource allocation policies with generative diffusion models (GDMs). We formulate the allocation problem as the maximization of an ergodic utility function subject…

Network flows often exhibit a hierarchical tree-like structure that can be attributed to the minimisation of dissipation. The common feature of such systems is a single source and multiple sinks (or vice versa). In contrast, here we study…

A large variety of real systems are composed by entities in relationships which can be represented by networks. In many of these systems, elements are embedded in the space and location information impacts properties and evolution. Local…

Climate change is reshaping species interactions and movement across fragmented landscapes. Despite this, most mathematical models assume random diffusion, overlooking the influence of directed movement. Here, we develop a graph based…

This paper focuses on the problem of growing multiplex networks. Currently, the results on the joint degree distribution of growing multiplex networks present in the literature pertain to the case of two layers, and are confined to the…

Diffusion-based algorithms have emerged as promising techniques for weight generation. However, existing solutions are limited by two challenges: generalizability and local target assignment. The former arises from the inherent lack of…

We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…