In network graph analysis, transport connectivity is evaluated using topological metrics. … — JAMB UTME

In network graph analysis, transport connectivity is evaluated using topological metrics. If a regional transport network consists of $4$ settlement nodes (vertices) linked by $6$ direct road corridors (edges), what is the Beta index ( $\beta$ ) of connectivity for this network?

A
$0.67$
$1.5$ Answer
C
$2.0$
D
$24.0$

Answer

The Beta index (

\beta

) of the network is

1.5

The Beta index (

\beta

) measures graph connectivity by taking the ratio of the total number of edges (

e

) to the total number of vertices (

v

). Dividing

6

edges by

4

vertices yields

\beta = 1.5

, indicating a highly connected network where nodes have on average

1.5

connecting routes.

Step-by-Step Solution

Identify the given topological values from the problem statement

Number of edges (

e

) =

6

, number of vertices (

v

) =

4

Topological connectivity analysis requires identifying total links (edges) and total nodes (vertices).

Apply the Beta index formula

\beta = \frac{e}{v}

The Beta index measures the average number of edges per vertex in a transport graph.

Substitute the values and compute the ratio

\beta = \frac{6}{4} = 1.5

Dividing

6

edges by

4

vertices gives a connectivity value of

1.5

Key Concept

Beta Index (

\beta

) Calculation in Network Graph Analysis

Estimated Time:45s

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