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Difficulty: HardTransportation Modes and Network Connectivity

In transportation geography, graph theory and topological metrics are used to measure network efficiency, structure, and connectivity. Match each network connectivity metric or concept on the left with its corresponding mathematical formula or structural definition on the right.

  • Beta Index (β\beta)Calculates simple network complexity by taking the ratio of total links to total vertices (β=ev\beta = \frac{e}{v}).
  • Gamma Index (γ\gamma)Measures the degree of network completeness by comparing actual links to the maximum possible links in a planar network (γ=e3(v−2)\gamma = \frac{e}{3(v - 2)}).
  • Alpha Index (α\alpha)Evaluates network circuitness by calculating the ratio of actual independent cycles to the maximum theoretical cycles (α=e−v+12v−5\alpha = \frac{e - v + 1}{2v - 5}).
  • Nodal AccessibilityQuantifies the relative ease with which a specific vertex can be reached from all other vertices in the network graph.

Answer

Beta Index matches with link-to-vertex ratio calculation; Gamma Index matches with planar graph completeness calculation; Alpha Index matches with circuitness/cycle ratio calculation; Nodal Accessibility matches with the ease of reaching a vertex from all other points.
Each transport graph index uniquely describes a topological dimension of a transportation network. The Beta Index (β=e/v\beta = e/v) measures simple connectivity/density; the Gamma Index (γ\gamma) evaluates network completeness against maximum planar connections; the Alpha Index (α\alpha) measures circuit redundancy; and Nodal Accessibility describes the ease of reaching a vertex from all other nodes.

Step-by-Step Solution

1
Identify the definition of Beta Index
Beta Index (β\beta) is computed as β=ev\beta = \frac{e}{v}, representing basic network linkage per node.
Beta index evaluates simple network structure without considering planar geometry limits.
2
Identify the definition of Gamma Index
Gamma Index (γ\gamma) compares actual edges ee to maximum planar edges 3(v−2)3(v-2).
In a planar network graph, no two edges cross without creating a vertex; maximum link potential is 3(v−2)3(v-2).
3
Identify the definition of Alpha Index
Alpha Index (α\alpha) evaluates circuitness via α=e−v+12v−5\alpha = \frac{e - v + 1}{2v - 5}.
Redundant routes or loops in a network are measured by independent cycles u=e−v+1u = e - v + 1 relative to maximum possible cycles.
4
Identify Nodal Accessibility
Nodal Accessibility represents the spatial centrality and path convenience of a specific vertex in relation to the whole system.
Accessibility is a property of a single node relative to the entire connectivity matrix of the transport network.

Key Concept

Topological Network Connectivity Indices in Transport Geography
Estimated Time:2m 0s
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Topics

Transportation Modes and Network Connectivity

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