The aim of this note is to call attention to a simple regularity regarding the number of walks in a finite graph G. Let W k denote the number of walks of length k(>= 0) in G. Then W a + b 2 =< W 2 a W 2 b holds for all a, b ε N 0 while equality holds exclusively either (I) for all a, b ε N0 (in case G is a regular graph), or(II) for all a, b ε N, or(III) for all a, b ε N 0 of equal parity (provided G is connected, this holds if and only if G is nonregular, yet semiregular graph), or(IV) for all a, b ε N of equal parity, or(V) just for a = b only. We show that all of these five cases can actually occur and discuss the resulting classification graphs in exactly five classes.