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Composition as an Evolving EntityComposition as an Evolving Entity envisions a work in continuous transformation, never reaching an equilibrium, a complex structure whose components permanently fluctuate and adjust to global changes. The process never produces a definitive version, but does provide at any arbitrary point in time a plausible variant of the work - a transitory being. Directed Graphs are used to represent the structural levels of a composition (vertices) and the relationships between them (edges); parent-children and ancestor-descendant types of connections de- scribe well potential hierarchies in a piece of music. By determining adjacencies and degrees of vertices and by introducing weights for edges, one can define affinities and dependencies in the complex and flexible structure that is a musical composition. Ways in which the all-incidence matrix of a graph with weighted edges can evolve are discussed including the use for that purpose of elements of Information Theory. Composition as an Evolving Entity model is closer the other paradigms to the way composers actually compose and refine their out- put; it also creates the equivalent of a live organism, growing, developing, and transforming itself over time.