The causal network is a possible description of complex phenomena, and several domains, for example, Machine Learning, Social Science, and Artificial Intelligence. Although a successful solution is referred to in this paper, the field inherently faces challenges. Among these, the work identified that the formalism used is time-consuming and difficult to understand. Consequently, the approach proposed in this paper consists in transcribing this formalism in a tensor form. This goal is accomplished in three steps: first common tensor formulas are proposed for direct and inverse models; second these formulas are adapted for the network primitives; in the end the primitive and consequently the formula composition is analysed. To facilitate the understanding of the proposed formalism, the paper describes several examples. This paper is dedicated to Prof. Imre J. Rudas, to celebrate his 75^th anniversary.