**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Publication# Existence, cost and robustness of spatial small-world networks

Abstract

Small-world networks embedded in Euclidean space represent useful cartoon models for a number of real systems such as electronic circuits, communication systems, the large-scale brain architecture and others. Since the small-world behavior relies on the presence of long-range connections that are likely to have a cost which is a growing function of the length, we explore whether it is possible to choose suitable probability distributions for the shortcut lengths so as to preserve the small-world feature and, at the same time, to minimize the network cost. The flow distribution for such networks, and their robustness, are also investigated.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related MOOCs (1)

Related concepts (32)

Related publications (32)

Ontological neighbourhood

Introduction to optimization on smooth manifolds: first order methods

Learn to optimize on smooth, nonlinear spaces: Join us to build your foundations (starting at "what is a manifold?") and confidently implement your first algorithm (Riemannian gradient descent).

Network theory

In mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the nodes or edges possess attributes. Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) components. Network theory has applications in many disciplines, including statistical physics, particle physics, computer science, electrical engineering, biology, archaeology, linguistics, economics, finance, operations research, climatology, ecology, public health, sociology, psychology, and neuroscience.

Complex network

In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research (since 2000) inspired largely by empirical findings of real-world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks.

Small-world network

A small-world network is a mathematical graph in which most nodes are not neighbors of one another, but the neighbors of any given node are likely to be neighbors of each other. Due to this, most neighboring nodes can be reached from every other node by a small number of hops or steps. Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes (the number of steps required) grows proportionally to the logarithm of the number of nodes N in the network, that is: while the global clustering coefficient is not small.

Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogenei ...

Nicolas Aspert, Volodymyr Miz, Benjamin Ricaud

Studying real-world networks such as social networks or web networks is a challenge. These networks often combine a complex, highly connected structure together with a large size. We propose a new approach for large scale networks that is able to automatic ...

2020In time-sensitive networks, regulators can be used to reshape traffic, and their usage may be necessary to guarantee stability by providing worst-case delay bounds. In this project, I study partial regulation of time-sensitive networks with cyclic dependen ...

2020