According to CLRS,
When the edges of the graph are static—not changing over time—we can compute the connected components faster by using depth-first search.
However, I tried to do some runtime analysis, and in a graph $G(V, E)$ on which we have to answer $Q$ connectivity queries.
DFS would take $O(V+E)$ asymptotic time to calculate the connected components, followed by $O(1)$ to answer each query, which leads to a total running time of $O(V+E+Q)$.
Whereas, an optimised Union Find would take $O(E.α(V))$ time to “add” all the edges, followed by $O(α(V))$ per query, which gives a total running time of $O(α(V).(E+Q))$.
Now, as we, know $α$ can be taken to be a constant factor for all practically conceivable applications, so Union Find works out to be faster, hence I am confused as to why the authors of CLRS call DFS faster.
Am I making a mistake with my analysis somewhere?