1. A computer-implemented method for analyzing costs associated with a cost flow model having components of relationships and entities, comprising: receiving data associated with the cost flow model that identifies the costs associated with the relationships among the entities; creating one or more matrices that are representative of the costs and the entity relationships; performing one or more sparse matrix operations upon the created one or more matrices in order to determine cost contribution amounts from an entity to another entity; providing to a user or an external system the determined cost contribution amounts for the entities.