A regional transport planning board mapped a single continuous railway network (p = 1) con… — JAMB UTME

A regional transport planning board mapped a single continuous railway network ( $p = 1$ ) connecting $15$ key industrial towns ( $v = 15$ ) with $22$ direct rail tracks ( $e = 22$ ). What is the cyclomatic number ( $C$ ) of this transport network?

Answer: 8

Answer

The cyclomatic number of the transport network is 8.

The cyclomatic number (

C

) measures structural redundancy and closed loops within a graph network using the standard topological equation

C = e - v + p

. Substituting

e = 22

v = 15

, and

p = 1

gives

22 - 15 + 1 = 8

, representing

8

independent loops in the network.

Step-by-Step Solution

Identify given network variables from the problem stem

e = 22

(edges/tracks),

v = 15

(vertices/towns),

p = 1

(connected component)

Topological indices require accurate counting of fundamental structural elements.

Apply the formula for the cyclomatic number

C = e - v + p

The cyclomatic number measures the number of fundamental circuits or redundant loops in a transport graph.

Compute the quantitative value

C = 22 - 15 + 1 = 8

Subtracting vertices from edges and adding the component count yields the exact number of independent loops.

Key Concept

Cyclomatic Number in Transport Network Analysis

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