Stoichiometric Network Analysis (SNA), originally developed by the Canadian chemist Bruce L. Clarke during the 1970s, provides a most efficient means of reducing the background topology of complex interaction networks to some skeleton topology around which systems dynamics can be understood without jeopardising insight into complex dynamics by over- or miss-simplification. Since it focuses on the corresponding autocatalytic (AC) features of a feedback system as those which control overall behaviour to some extent, SNA deals with reaction kinetics in and beyond chemistry, e.g. with nuclear reactions. It is therefore quite straightforward to apply this manner of simplification, which in turn is supported by a number of mathematical theorems on systems behaviour and properties of AC cycles, to biological systems although their 'full' complexity may not even be assessed in the yet rare cases of complete genetic sequencing. Assuming there is a relationship between the kinds of metal or metalloid species and key biological/biochemical transformations to be promoted with their aid--this relationship being the subject of bio-inorganic chemistry--and that biochemistry is, in effect, about systems which can reproduce and thus behave autocatalytically, one can expect SNA to yield formally sound statements on basic features of biology and biochemistry too. If we sum up the facts and considerations concerning essentiality or possible essentiality in a biological system of elements (Markert, 1994), this means joining the triangular representation of BSE, including statements on (the degree of biological) evolution and aggregation levels, to SNA treatment of autocatalysis within hierarchical systems from metalloenzymes to entire biocoenoses. Arguments using preferred cluster sizes and aggregation tendencies from coordination chemistry are then employed to circumscribe possible functions within the BSE. They are also extended to metals hitherto not known to be essential, such as tellurium or scandium.