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When droplets are tightly packed in a 2D microchannel, coalescence of a pairof droplets can trigger an avalanche of coalescence events that propagatethrough the entire emulsion. This propagation is found to be stochastic, i.e.every coalescence event does not necessarily trigger another. To study how thelocal probabilistic propagation affects the dynamics of the avalanche, as awhole, a stochastic agent based model is used. Taking as input, i) how thedroplets are packed (configuration) and ii) a measure of local probabilisticpropagation (experimentally derived; function of fluid and other systemparameters), the model predicts the expected size distribution of avalanches.In this article, we investigate how droplet configuration affects the avalanchedynamics. We find the mean size of these avalanches to depend non-trivially onhow droplets are packed together. Large variations in the avalanche dynamicsare observed when droplet packing are different, even when the other systemproperties (number of droplets, fluid properties, channel geometry, etc.) arekept constant. Bidisperse emulsions show less variation in the dynamics andthey are surprisingly more stable than monodisperse emulsions. To get asystems-level understanding of how a given droplet-configuration eitherfacilitates or impedes the propagation of an avalanche, we employ agraph-theoretic analysis, where emulsions are expressed as graphs. We find thatthe properties of the underlying graph, namely the mean degree and thealgebraic connectivity, are well correlated with the observed avalanchedynamics. We exploit this dependence to derive a data-based model that predictsthe expected avalanche sizes from the properties of the graph.

Inferring the stability of concentrated emulsions from droplet configuration information