Spatial Networks

  title={Spatial Networks},
  author={Marc Barthelemy},
  booktitle={Encyclopedia of Social Network Analysis and Mining},
  • M. Barthelemy
  • Published in
    Encyclopedia of Social…
    2 October 2010
  • Computer Science

Random Spatial Networks: Small Worlds without Clustering, Traveling Waves, and Hop-and-Spread Disease Dynamics

A class of random spatial networks (RSNs) is introduced which generalizes many existing random network models but adds spatial structure, and is used to propose a new generalization of small-world networks, where the average shortest path lengths in the graph are small, but with close spatial proximity of nodes that are neighbors in the network playing the role of large clustering.

From Complex to Spatial Networks

This chapter describes briefly the evolution of these fields and ideas about spatial networks, most of these objects are planar and in the second part of this chapter, the basic definitions and results for planar graphs.

Complex contagions on noisy geometric networks

This work addresses the question of when contagions spread predominantly via the spatial propagation of wavefronts rather than via the appearance of spatially-distant clusters of contagion (as observed for modern epidemics) and finds a deep connection between the fields of dynamical systems and nonlinear dimension reduction.

Spatial structure of complex network and diffusion dynamics

In the recent development of network sciences, spatial constrained networks have become an object of extensive investigation. Spatial constrained networks are embedded in configuration space. Their

Spatial community structure and epidemics

The results indicate that it is important to incorporate spatial information intonull models for community detection, but it is best to incorporate only relevant information into null models, as extraneous information can lower performance.

A Latent Parameter Node-Centric Model for Spatial Networks

A novel model for capturing the interaction between spatial effects and network structure is introduced which attaches a latent variable to each node which represents a node's spatial reach and is inferred from the network structure using a Markov Chain Monte Carlo algorithm.

Temporal Networks

Spatial optimality in power distribution networks

This paper investigates the effect of the wiring cost in the spatial organization of a sample of power distribution networks by means of shuffling the networks in systematic ways and shows that although they share similar topologies, suboptimal networks seem to accumulate more failures.

Modeling spatial social complex networks for dynamical processes

A spatial social complex network (SSCN) model is developed that captures not only essential connectivity features of real-life social networks, including a heavy-tailed degree distribution and high clustering, but also the spatial location of individuals, reproducing Zipf's law for the distribution of city populations as well as other observed hallmarks.

Emergence of hierarchy in cost-driven growth of spatial networks

A generic model for the growth of spatial networks based on the general concept of cost–benefit analysis is introduced and it is shown that spatial hierarchy emerges naturally, with structures composed of various hubs controlling geographically separated service areas, and appears as a large-scale consequence of local cost– benefit considerations.



The architecture of complex weighted networks.

This work studies the scientific collaboration network and the world-wide air-transportation network, which are representative examples of social and large infrastructure systems, respectively, and defines appropriate metrics combining weighted and topological observables that enable it to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices.

Connectivity distribution of spatial networks.

It is shown that for regular spatial densities, the corresponding spatial network has a connectivity distribution decreasing faster than an exponential, and that scale-free networks with a power law decreasing connectivity distribution are obtained when a certain information measure of the node distribution diverges.

Evolution of networks

The recent rapid progress in the statistical physics of evolving networks is reviewed, and how growing networks self-organize into scale-free structures is discussed, and the role of the mechanism of preferential linking is investigated.

Structural properties of spatially embedded networks

The results indicate that spatial constrains have a significant impact on the network properties, a fact that should be taken into account when modeling complex networks.

Vulnerability of weighted networks

The analysis of weighted properties shows that centrality driven attacks are capable of shattering the network’s communication or transport properties even at a very low level of damage in the connectivity pattern and the inclusion of weight and traffic provides evidence for the extreme vulnerability of complex networks to any targeted strategy.

The effects of spatial constraints on the evolution of weighted complex networks

The presented results suggest that the interplay between weight dynamics and spatial constraints is a key ingredient in order to understand the formation of real-world weighted networks.

Public transport networks: empirical analysis and modeling

A simple model reproduces many of the identified PTN properties by growing networks of attractive self-avoiding walks, including a surprising geometrical behavior with respect to the two-dimensional geographical embedding and an unexpected attraction between transport routes.

Complex Networks: Structure and Dynamics

The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.

Assessing the relevance of node features for network structure

This paper proposes a general indicator Θ, based on entropy measures, to quantify the dependence of a network's structure on a given set of features, and applies this method to social networks of friendships in U.S. schools, to the protein-interaction network of Saccharomyces cerevisiae and to the U.s. airport network, showing that the proposed measure provides information that complements other known measures.

Hyperbolic Geometry of Complex Networks

It is shown that targeted transport processes without global topology knowledge are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure.