In transport network analysis, a geographic planner models a regional planar road network … — JAMB UTME

In transport network analysis, a geographic planner models a regional planar road network connecting $6$ primary market towns ( $v = 6$ ) via $9$ direct road links ( $e = 9$ ). What is the Gamma index ( $\gamma$ ) of connectivity for this transportation network?

$0.75$ Answer
B
$1.50$
C
$0.50$
D
$0.60$

Answer

The Gamma index ($\gamma$) of connectivity for the transportation network is

0.75

(or

75\%

The Gamma index ($\gamma$) represents the relationship between the actual number of edges (

e

) in a network and the maximum possible number of edges (

e_{\text{max}}

) for a planar graph, expressed by the formula

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

. Given

v = 6

nodes and

e = 9

edges, substituting these values yields

\frac{9}{3(6 - 2)} = \frac{9}{12} = 0.75

Step-by-Step Solution

Identify the given network graph parameters

Number of vertices (

v

) =

6

, number of edges (

e

) =

9

Topological indices require the count of nodes and links in the network.

Apply the planar Gamma index formula

\gamma = \frac{e}{e_{\text{max}}} = \frac{e}{3(v - 2)}

The Gamma index measures the ratio of actual edges to the maximum possible number of edges in a planar graph.

Substitute values into the formula and solve

\gamma = \frac{9}{3(6 - 2)} = \frac{9}{3 \times 4} = \frac{9}{12} = 0.75

Simplifying the numerical expression gives the fractional connectivity score.

Key Concept

Gamma Index of Network Connectivity

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