with a high number of discrete states to a model with fewer states generically demands a non-Markovian description. Therefore, in continuation of previous work [@Prager2003; @PrFaSchiZa07; @Prager2007] in this paper a semi-Markovian model [@cox1962renewal] of stochastic two-state units is considered. As a new point of interest these units are embedded in an uncorrelated random network whose nodes possess different but independent degrees, in particular this excludes networks with high asortativity or dissortativity. The structure of the network is given by the node distribution $p(k)$. A big number of nodes is assumed, it is known that finite size effects [@Pinto2014] have a strong effect on the dynamic of the stochastic process as well as on the network influence. Complex networks are of top interest in statistical physics because it allows deviation from global coupling without specification of a spatial structure as well as providing a framework to map complex spatial structures to an abstract space. Furthermore, network structures are present in many situations of everyday life, for example transport [@Barrat2004; @Jiang2007; @Mukherjee2003] and supply networks [@Runions2005] to mention just a few.

The paper is structured as follows. In Section \[sec:MF\] the master equations for stochastic two-state units are derived. In Section 