goes over rational numbers. The assumption is made that the probability to have an edge between the $i$th and $j$th node is proportional to the product of the degrees of these nodes, i.e., to $k_i\,k_j$. This is strictly valid only for uncorrelated networks. Further on, taking into account the conservation of degree as required in the following replacing for a fully connected network is defined $$\tilde{A}_{ij} =  \frac{ k_i\, k_j}{\sum_{l=1}^{N} k_{l}}.
  \label{eq:newA}$$ Figure \[fig:HMF\] illustrates the replacement. As a result the single nodes with given degree $k$ couple uniquely to a mean filed. Hence, in contrast to the original network, the fully connected network will allow a mean-field representation with respect to all edges with coinciding degrees $k$. In [@Sonnenschein2012] the validity of this replacement procedure was discussed and it was successfully applied to complex networks with continuous phase oscillators at the nodes. The approach [@Ichinomiya2004; @Sonnenschein2012; @Carro2016] is here generalized to discrete stochastic two state units.

![Representation of a random binary network with $k_1=12$, $k_2=6$ and $N=25$ before and after applying the heterogeneous mean-field approximation.[]{data-label="fig:HMF"}](GraphVis_mf2_N-25_beta1-0-5-alpha-2_nu-0-34.pdf){width="\linewidth"}

As a result of the replacement, the signal function in is approximated as $$\tilde{f}_i(t)\approx\frac{1}{N}\sum_{j=1}^N \tilde{A}_{ij}s_j(t)=\frac{k_i}{N\sum_{l=1}^{N}k_{l}}\sum_{j=1}^{N}k_j s_j(t).
  \label{eq:newoutput}$$ It follows immediately, that the signal at 