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The formation of cosmic structure results from the action of gravity on matter in an expanding Universe. As the evolution proceeds, the velocity field changes from being single-valued almost everywhere in space to being multi-valued over a complex web of `multistreaming' regions associated with the formation of large-scale structure (LSS) such as halos (or clumps), filaments, and sheets. Until recently, these structures have been investigated primarily via the (scalar) mass density field. In this application paper we apply data analysis and visualization techniques to cosmological simulations with the aim of studying multistreaming regions using velocity-based probes. Compared to the current practice of using density information (e.g., morphology estimators, locating overdense regions with halo finders), we show that velocity-based methods can provide useful supporting, as well as complementary, information. Because the density field and multistreaming are correlated but do not contain the same information, new and interesting information about the properties of the large-scale structure may be extracted, e.g., capturing dynamical behavior not possible with density-based estimators. Incorporating a novel method for setting thresholds for the velocity-based estimators, we study the relationships between the density field as represented by compact overdense halos and the different properties of multistreaming regions as represented by different velocity-based estimators.