On polynomial digraphs

Let Φ(x,y)Φ(x,y) be a bivariate polynomial with complex coefficients. The zeroes of Φ(x,y)Φ(x,y) are given a combinatorial structure by considering them as arcs of a directed graph G(Φ)G(Φ). This paper studies some relationship between the polynomial Φ(x,y)Φ(x,y) and the structure of G(Φ)G(Φ).