Algorithm to recognize Strongly Regular Graph (SRG)
There is a trivial $O(kn^2)$ algorithm:


Choose a vertex $v$ and calculate its degree $k$. Then verify that all other vertices have degree $k$.
Choose some neighbor $w$ of $v$ and calculate the number of common neighbors $\lambda$. Then verify that all other pairs of adjacent vertices have $\lambda$ common neighbors.
Choose some non-neighbor $x$ of $v$ and calculate the number of common neigbors $\mu$. Then verify that all other pairs of non-adjacent vertices have $\mu$ common neighbors.


If you like linear algebra, you can also compute the square $A^2$ of the adjacency matrix $A$. Then check that:


All diagonal entries of $A^2$ are equal to some constant $k$.
All off-diagonal entries $A^2_{ij}$ such that $A_{ij} = 1$ are equal to some constant $\lambda.
All off-diagonal entries $A^2_{ij}$ such that $A_{ij} = 0$ are equal to some constant $\mu$.


This algorithm takes time $O(n^\omega)$.