We have a star network. It consists of one central node and 9 peripheral nodes. That is a hub that is connected to 9 nodes. What is the density of this network?

The network density is defined in network analysis as that of the ratio of observed connections to the number of potential connections for just a network system, and further calculation can be defined as follows:

Whenever the number of current relationships is small in comparison to the total number of prospective ties.
Dense connections are much more vital in controlling and punishing than they are for communicating data, and it also produces a great deal of data redundancy.

Calculation:

Node(n)=9

actual connection= 9

calculating the potential connections by using formula:

[tex]\bold{= \frac{n \times (n-1)}{2}}\\\\=\frac{9 \times (9-1)}{2} \\\\=\frac{9 \times 8}{2}\\\\= \frac{72}{2}\\\\= 36[/tex]

Calculating the network density:

[tex]\text{Network density}=\frac{\text{Actual connection}}{\text{potential connections}}[/tex]

[tex]\bold{=\frac{9}{36}}\\\\\bold{=\frac{1}{4}}\\\\\bold{=0.25}\\\\[/tex]

Calculating the network density percentage:

[tex]\bold{=0.25 \times 100}\\\\ \bold{=25\%}\\\\[/tex]

Therefore, the network density is "25%".

Please find the graph in the attachment.

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