You have $8$ vertices, labelled $2$, $3$, and so on. Now we need to determine the edges.
Look for example at the vertices $2$ and $3$. Are they joined by an edge? They are to be joined precisely if $\gcd(2,3)=1$. The greatest common divisor of $2$ and $3$ is indeed $1$, so draw an edge joining $2$ and $3$.
Are vertices $2$ and $4$ joined by an edge? Well, $\gcd(2,4)=2\ne 1$, so no edge.
Are vertices $2$ and $5$ joined by an edge? Yes, because $\gcd(2,5)=1$. Continue.
Vertex $2$ will be joined to $3$, $5$, $11$, $13$. Now we have produced all the edges that involve $2$.
In addition, $3$ is joined to $4$, $5$, $11$, $13$, $14$.
In addition, $4$ is joined to $5$, $11$, and $13$.
In addition, $5$ is joined to $11$, $12$, $13$, $14$.
In addition, $11$ is joined to $12$, $13$, $14$.
In addition, $12$ is joined to $13$.
And finally, $13$ is joined to $14$.