where $K(v) \leq i < K(v+1)$. Then the connectivity of $v$ is $K(v+1)-K(v)$. This defines the array $K$, with the rules $K(1) =
1$ and $K(N+1) = 2L+1$.

Note that each edge $\{v,w\}$ appears twice in $T$: once for $v$ and once for $w$. This requires twice more memory than a storage method exploiting the symmetry of the matrix (in which the edges appear only once), but the computational task is faster because the adjacent vertices of a given vertex are simply obtained from arrays $T$ and $K$.

The leaf removal process is done leaf by leaf. Each time a leaf is removed, the adjacent vertices are examined: if new leaves appear, there are added to a list of potential leaves to be considered later. Each elementary leaf removal requires a computational time of order $O(1)$ and not $O(N)$. So the computational time for the global leaf removal is proportional to the number of removed leaves, which is bounded by $N/2$. Then the total computational time for one random graph (generation and leaf removing) is $N$ times a function of $\alpha$.

For each random graph, we have measured the number of isolated points $|I|$, the size (number of vertices) of 