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We extend previous work on injectivity in chemical reaction networks togeneral interaction networks. Matrix- and graph-theoretic conditions forinjectivity of these systems are presented. A particular signed, directed,labelled, bipartite multigraph, termed the ``DSR graph'', is shown to be auseful representation of an interaction network when discussing questions ofinjectivity. A graph-theoretic condition, developed previously in the contextof chemical reaction networks, is shown to be sufficient to guaranteeinjectivity for a large class of systems. The graph-theoretic condition issimple to state and often easy to check. Examples are presented to illustratethe wide applicability of the theory developed.

Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements