 With the aim of still enlarging the range of application of algebraic fibring, so as to make it able to deal with substructural logics and with logics endowed with nondeterministic semantics, as well as to combine pointwise models of each logic, a formalism for representing logics and their combinations based on the general notion of multi-graphs (or, for short, m-graphs) was proposed by A. Sernadas and his collaborators (see Sernadas et al. 2009a, 2009b). Multi-graphs are graphs where the source of each edge is a finite sequence of nodes (instead of a unique node). Concerning signatures, the nodes of the m-graph are seen as sorts and the m-edges are seen as language constructors. From the semantical viewpoint, nodes are truth-values and m-edges are relations between truth-values. Finally, concerning deductive systems, nodes are language expressions, and m-edges are inference rules. The fibring of logics described by m-graphs (a.k.a. graph-theoretic fibring) is defined by pointwise combining models of each combined logic, in contrast to the usual notion of semantic fibring in which entire classes of models are combined. This allows one to avoid the collapsing problem (see the next section) in a very natural way.