**Abstract** : Emergy is becoming an important sustainability ratio. Emergy analysis of real systems cannot be summarized to the trivial analysis of systems with several sources and one product. In such case only the application of the first rule of emergy algebra (all sources of emergy to a process are assigned to the process output) is required and the result can be stored in a simple table.
But real systems of interest (ecosystems, complex chemical production systems, etc) are interconnected systems with feedbacks, splits and by-products. As a consequence mathematical foundations for exact emergy analysis appear to be necessary. Indeed, emergy computation within an energy system diagram is based on four rules, the use of which is sometimes confusing. The complexity of the computation of emergy within interconnected system comes also from the fact that it does not obey Kirchoff-like circuit law. Thus, linear algebra approach fails.
Emergy computation follows a logic of memorization, thus the evaluation principles deal with pathways. An emergy pathway is a pathway from a source of emergy to a product which represents the sequel of assignations of the emergy source by the processes of the interconnected system.
Looking at pathways in ecosystems analysis is not a new subject. Because of the rules of emergy computation (specifically the no double counting rule) among an abundant classification of pathways in ecosystems the emergy pathways appear to be particular elements of only two classes of pathways: the class of simple pathways and the class of terminal non-feedback cycle pathways.
This paper is the companion paper of a previous paper written by the same authors. In the previous paper it is explained how to compute emergy flowing on a given arc of an emergy graph assuming all emergy pathways ending by this arc known. As explained in this paper an emergy graph is a transformed graph from an energy system diagram.
The aims of this paper are as follows. (i) Explain how to transform an energy system diagram into an emergy graph. (ii) Provide a clear and new algorithm easily programmable to compute emergy pathways. (iii) Insert this new algorithm in the whole procedure for computing an emergy flowing between two processes. (iv) Apply the whole procedure on a real world example. This example shows that the emergy content from meadowland-sun can either carry out by the milk or by the electricity (when considering the biogas and the CHP plant). In the general case, this emergy amount is lesser than the total meadowland-sun emergy.