Centrality Analysis

Betweenness, Closeness, Straightness, Degree Centrality

In graph theory, centrality estimates to determine the hierarchy of nodes or edge within a network. The centrality analysis uses for diverse urban scales for local and global. A local centrality defines the distance between nodes within a given radius and a global centrality calculates the distance between nodes in a whole system. The Centrality Index is useful to understand the operational analysis of network flow tendency in transportation geographies, such as airline networks, road networks, and canal networks. As well as it measures to understand a node (location) importance in space.

Source: Based on Wikipedia A) Betweenness, B) Closeness, C) Degree

Evaluations by NNA Toolbox for Cambridge areas, MA

Betweenness

The Betweenness Index is the total number of shortest paths (N) at the target location (k) divided by the total number of shortest paths that exist between two nodes (i and j) of a given radius (r).

The target node (k) would have a high betweenness centrality if it appears in many shortest paths to the node that estimates realistic pedestrian flows in the network.

Source: Based on Freeman (1977)

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Closeness

The Closeness Index indicates how close an origin (i) is to all other destinations (j) in a given radius (r). It is calculated as the average of the shortest path length from the node (i) to every other node (j) in a given radius (r). The shortest path is to use Euclidean distance.

Lower values indicate more central nodes. If node D’s proximity centrality is 1.5 and node A is 3.5, so node D is more central in this measure.

Source: Based on Sabidussi (1966)

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Straightness

The Straightness Index refers to the hypothesis that the connectivity between two points (i, j) is better when the path is straight. d^Eu is the Euclidean distance between i and j along a straight path. d[i,j] is the shortest path distance between i and j.

The higher the straightness index, the higher the efficiency and the straightness centrality linking to destinations.

Source: Based on Porta, Crucitti et al (2005)

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Degree

The Degree Centrality Index is a count of the total number of connecting edges (N) to a node (i) in a given radius (r).

A higher Degree Index means that one node (i) is more connected to another node. The lower the Degree Index, the more evenly connected in the network.

Source: Based on Freeman (1979)

No. connectivity at each node

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