Spatial Networks

Synonyms

Network geography; Space-embedded networks;

Transportation systems; Urban networks

Glossary

Graph:

(or Network) A set of vertices connected by edges

Adjacency Matrix:

A matrix A which represents the structure of a graph. The element A _ij is either 0 if i and j are not connected or A _ij = 1 if there is an edge from i to j. For a spatial network, the position of the nodes {x _i } is needed in order to completely characterize the network

Betweenness Centrality:

The betweenness centrality of a vertex (or an edge) x is defined as $BC(x) = \sum\nolimits_{s,t \in V} {{{\sigma _{st} (x)} \over {\sigma _{st} }}}$ where σ _st .(x) is the number of shortest paths between s and t using x and σ _st is the number of all shortest paths between s and t

Betweenness Centrality Impact:

Measures how a new link affects the average betweenness centrality of a graph. This quantity can help in characterizing the different types of new links during the evolution of a (spatial) network

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