Centrality Measures in Spatial Networks of Urban Streets

The map of a city's streets constitutes a particular case of spatial complex network. However a city is not limited to its topology: it is above all a geometrical object whose particularity is to organize into short and long axes called streets. In this article we present and discuss two algorithms aiming at recovering the notion of street from a graph representation of a city. Then we show that the length of the so-called streets scales logarithmically. This phenomenon leads...

The dynamics of transportation through towns and cities is strongly affected by the topology of the connections and routes. The current work describes an approach combining complex networks and self-avoiding random walk dynamics in order to quantify in objective and accurate manner, along a range of spatial scales, the accessibility of places in towns and cities. The transition probabilities are estimated for several lengths of the walks and used to calculate the outward acce...

Cities can be seen as the epitome of complex systems. They arise from a set of interactions and components so diverse that is almost impossible to describe them exhaustively. Amid this diversity, we chose an object which orchestrates the development and use of an urban area : the road network. Following the established work on space syntax, we represent road networks as graphs. From this symbolic representation we can build a geographical object called the way. The way is def...

Experts from several disciplines have been widely using centrality measures for analyzing large as well as complex networks. These measures rank nodes/edges in networks by quantifying a notion of the importance of nodes/edges. Ranking aids in identifying important and crucial actors in networks. In this chapter, we summarize some of the centrality measures that are extensively applied for mining social network data. We also discuss various directions of research related to th...

In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant advances in the understanding of the structure, formation and function of complex systems. Social and biological processes such as the dynamics of epidemics, the diffusion of information in social media, the interactions between species in ecosys...

Several natural and theoretical networks can be broken down into smaller portions, or subgraphs corresponding to neighborhoods. The more frequent of these neighborhoods can then be understood as motifs of the network, being therefore important for better characterizing and understanding of the overall structure. Several developments in network science have relied on this interesting concept, with ample applications in areas including systems biology, computational neuroscienc...

Spatial organisation of physical form of an urban system, or city, both manifests and influences the way its social form functions. Mathematical quantification of the spatial pattern of a city is, therefore, important for understanding various aspects of the system. In this work, a framework to characterise the spatial pattern of urban locations based on the idea of entropy maximisation is proposed. Three spatial length scales in the system with discerning interpretations in ...

A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of scale-free networks embedded by the suggested algorithm are studied both analytically and through simulations. Our findings indicate dramatic changes in the embedded networks, in comparison to their off-lattice counterparts, and call into question t...

A complex web of roads, walkways and public transport systems can hide areas of geographical isolation very difficult to analyze. Random walks are used to spot the structural details of urban fabric.

An urban road network of Le Mans in France is analyzed. Some topological properties of network are investigated, such as degree distribution, clustering coefficient, diameter, and characteristic path length. These results suggest that our network is a "small- world" network with short average shortest path and large clustering coefficient. Furthermore, double power-law distribution is found in degree distribution which is distinct from the single power-law and a novel degree ...