The paper presents a programmable triangular neighborhood function for application in low power transistor level implemented Kohonen self-organized maps (SOMs). Detailed simulations carried out for the software model of such network show that the triangular function forms a good approximation of the Gaussian function, while being implemented in a much easier way in hardware. The proposed circuit is very flexible and allows for easy adjustments of the slope of the function. It enables the asynchronous and fully parallel operation of all neurons in the network thus making it very fast. The proposed mechanism can be used in custom designed networks either in their analog or digital implementation. Due to the simple structure, the energy consumption per a single input pattern is low (120 pJ in case of the map of 16 x 16 neurons).