  In many complex systems, for the activity f(i) of the constituents or nodes
i, a power-law relationship was discovered between the standard deviation
sigma(i) and the average strength of the activity: sigma(i) ~ <f(i)>^alpha;
universal values alpha = 1/2 or 1 were found, however, with exceptions. With
the help of an impact variable we introduce a random walk model where the
activity is the product of the number of visitors at a node and their impact.
If the impact depends strongly on the node connectivity and the properties of
the carrying network are broadly distributed (like in a scale free network) we
find both analytically and numerically non-universal alpha values. The exponent
always crosses over to the universal value of 1 if the external drive
dominates.
