Generation of Spatially Embedded Random Networks to Model Complex Transportation Networks

Abstract

Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random networks, often without considering their spatial properties. In this article, a methodology is proposed to create random networks conserving their spatial properties. The produced random networks are not intended to be an accurate model of the real-world network being investigated, but are to be used to gain insight into the functioning of the network taking into consideration its spatial properties, which has potential to be useful in many types of analysis, e.g. estimating the network related risk. The proposed methodology combines a spatial non-homogeneous point process for vertex creation, which accounts for the spatial distribution of vertices, considering clustering effects of the network and a hybrid connection model for the edge creation. To illustrate the ability of the proposed methodology to be used to gain insight into a real world network, it is used to estimate standard structural statistics for part of the Swiss road network, and these are then compared with the known values.

Estimation of traffic flow changes using networks in networks approaches

“…In order to consider the influence of the different lower-order hypervertices on the connection between two hypervertices, connection models are used for the intra-layer edge assignment (Meester and Roy 1996;Hackl and Adey 2017;. A connection model M(G β , g β ) has two characteristics.…”

Large algebraic connectivity fluctuations in spatial network ensembles imply a predictive advantage from node location information

“…Models of within this class have been used in a diverse range of applications including: social networks [6][7][8], wireless communications networks [4,9,10], spatially constrained networks in the brain [11,12] and transport networks [13]. However, in practice, the amount of information that we possess about the graph structure can vary significantly.…”

“…In other cases we may possess coarse-grained data describing the density of individuals. For instance, population density contained within census data which has been used as an input for models of social networks [15,16] and transportation networks [13]. Furthermore, even when we do not possess data about individual nodes, we can often obtain their relative positions in some latent embedding space [17].…”

“…A wide range of real world systems can be modelled with ensembles of RGGs and their generalizations [1,2,[6][7][8][11][12][13]. These consist of both spatially embedded systems and graphs where the nodes posses other attributes which are relevant to tie formation.…”

“…The techniques used to derive 26 can in principle be extended to the case of general domains and connection functions. This can be achieved by choosing the desired connection function in equation (13) and then integrating w.r.t the desired node distribution in the corresponding domain. In many cases the resulting integral may not be tractable, however, this equation still provides some insight into the factors which effect the average value of µ 2 .…”