Transportation Geography and Network Science/Characterizing Graphs

< Transportation Geography and Network Science

beta index

The beta index ( $\beta$ ) measures the connectivity relating the number of edges to the number of nodes. It is given as:

$\beta=\frac{e}{v}$

where e = number of edges (links), v = number of vertices (nodes)

The greater the value of $\beta$ , the greater the connectivity. As transport networks develop and become more efficient, the value of $\beta$ should rise.

cyclomatic number

The cyclomatic number ( $u$ ) is the maximum number of independent cycles in a graph.

$u=e-v+p$

where p = number of graphs or subgraphs.

alpha index

The alpha index ( $\alpha$ ) is the ratio of the actual number of circuits in a network to the maximum possible number of circuits in that network. It is given as:

$\alpha=\frac{u}{2v-5}$

Values range from 0%—no circuits—to 100%—a completely interconnected network.

gamma index

The gamma index ( $\gamma$ ) measures the connectivity in a network. It is a measure of the ratio of the number of edges in a network to the maximum number possible in a planar network ( $3(v-2)$ )

$\gamma=\frac{e}{3(v-2)}$

The index ranges from 0 (no connections between nodes) to 1.0 (the maximum number of connections, with direct links between all the nodes).

Completeness

The number of links in a real world network is typically less than the maximum number of links and the completeness index used here captures this difference. This measure is estimated at the metropolitan level.

$\rho_{complete} = \frac{e}{e_{max}} = \frac{e}{{v^2}-{v}}$

$e$ refers to the number of links or street segments in the network and $v$ refers to the number of intersections or nodes in the network. Compare with the $\gamma$ index above.

König number

The König number (or associated number) is the number of edges from any node in a network to the furthest node from it. This is a topological measure of distance, in edges rather than in kilometres. A low associated number indicates a high degree of connectivity; the lower the König number, the greater the Centrality of that node.

eta index

The eta index ( $\eta$ ) measure the length of the graph over the number of edges.

$\eta=\frac{L(G)}{e}$

theta index

The theta index ( $\theta$ ) measure the traffic (Q(G)) per vertex.

$\theta=\frac{Q(G)}{v}$

iota index

The iota index ( $\iota$ ) measures the ratio between the length of its network and its weighted vertices.

$\iota=\frac{L(G)}{W(G)}$

$W(G)=1,\forall o=1$

$W(G)=\sum_{e}2*o,\forall o>1$

Source:

This article is issued from Wikibooks. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.