In this article, the authors consider the problem of approximating a complex network of linear dynamic systems by a simpler network, with the goal of highlighting the most significant connections. In other words, they explore the approximation of a network belonging to a certain class by another network of its class. \par From a technical perspective, in this work, the authors choose a class of dynamic networks with a directed tree (polytree) structure as a set of approximators and they derive an analytic technique to asymptotically satisfy the congruity property when the observation horizon approaches infinity. \par A linear dynamic influence model (LDIM) is defined as a pair $\Cal{G}=(H(z),u)$ where $u=(u_1,\dots,u_n)^\ss{T}$ is a vector of $n$ wide-sense stationary stochastic processes with finite variance, such that $\Phi_u(z)$, the power spectral density of $u$, is rational diagonal and positive definite for $|z|=1$, and $H(z)$ is an $n\times n$ matrix of rational causal and stable transfer functions with $H_{ii}(z)=0$ for $i=1,\dots,n$. The output process of the LDIM is $\{y_i\}_{i=1}^n$ such that $$ y_i=u_i+\sum_{j=1}^nH_{ij}(z)y_j. $$ \par Let $G$ be a directed graph. $G$ is a polytree graph if for every two nodes there is exactly one path connecting them. \par A formal statement of the problem which is studied in this paper is: Given the observations of the outputs $\{y_i\}_{i=1}^n$ of a generic LDIM $\Cal{G}$ with unknown structure, approximate the associated graph of $G$ with a simpler polytree, via an algorithm which is congruous in the skeleton and in the orientations, with respect to the class of linear dynamic polytrees. \par The main idea is to split the algorithm into two steps: \roster \item Determine the skeleton of the polytree approximating the LDIM structure. \item Assign orientations to the links of the polytree skeleton obtained. \endroster \par From a practical point of view, in order to test the tree approximation technique, the authors consider its application to the analysis of a stock portfolio.