A regional transportation network connects 6 major urban centers (vertices) using 9 direct… — JAMB UTME

A regional transportation network connects $6$ major urban centers (vertices) using $9$ direct highway corridors (edges). What is the Beta index of connectivity for this transport network?

$1.50$ Answer
B
$0.67$
C
$3.00$
D
$0.50$

Answer

The Beta index of connectivity for the transport network is

1.50

The Beta index (

\beta

) measures the simple connectivity of a transportation network using graph theory. It is computed as

\beta = \frac{\text{edges}}{\text{vertices}}

. With

9

edges and

6

vertices,

\beta = \frac{9}{6} = 1.50

. A Beta index greater than

1.0

indicates a connected network with circuits.

Step-by-Step Solution

Identify the number of vertices (

v

) and edges (

e

) in the transport network.

v = 6

(urban centers) and

e = 9

(highway corridors).

Topological graph metrics rely on identifying the basic structural components of a network.

Apply the Beta index formula for network connectivity.

\text{Beta index } (\beta) = \frac{e}{v}

The Beta index evaluates simple network connectivity by measuring the average number of edges per vertex.

Substitute the values into the formula and calculate.

\beta = \frac{9}{6} = 1.50

Dividing

9

6

gives

1.50

, indicating a moderately connected network.

Key Concept

Topological Network Connectivity Metrics (Beta Index)

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