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Structural balance is a classic property of signed graphs satisfying Heider'sseminal axioms. Mathematical sociologists have studied balance theory since itsinception in the 1040s. Recent research has focused on the development ofdynamic models explaining the emergence of structural balance. In this paper,we introduce a novel class of parsimonious dynamic models for structuralbalance based on an interpersonal influence process. Our proposed models aregradient flows of an energy function, called the dissonance function, whichcaptures the cognitive dissonance arising from violations of Heider's axioms.Thus, we build a new connection with the literature on energy landscapeminimization. This gradient flow characterization allows us to study thetransient and asymptotic behaviors of our model. We provide mathematical andnumerical results describing the critical points of the dissonance function.

Structural Balance via Gradient Flows over Signed Graphs