Bipartite and directed scale-free complex networks arising from zeta functions

•A new class of directed and bipartite complex networks is introduced.•They are related to multiple zeta functions.•A construction of scale-free networks is proposed.•Phase transitions for the models introduced are studied.

We construct a new class of directed and bipartite random graphs whose topology is governed by the analytic properties of multiple zeta functions. The bipartite L-graphs and the multiplicative zeta graphs are relevant examples of the proposed construction. Phase transitions and percolation thresholds for our models are determined.