Threshold functions are Boolean functions that model neurons, processing units of an artificial neural network. these functions can be represented geometrically as a unit hypercube in which each vertex is labeled either by 1 or 0. these representations can be simplified into graphs without losing the relationship between minterms and vertices. A graph labeling can be used to store threshold functions as well as to keep the relation between minterms and vertices.there are store threshold functions as well as to keep the relation between minterms and vertices. there are 119 different graphs that represent all of the 95,572 threshold functions of five variables. this paper presents graphs of threshold functions and some patterns followed by these graphs fo mall number of minters and variables and some open problems.