Complex networks and SOA: Mathematical modelling of granularity based web service compositions

Service Oriented Architecture (SOA) can be defined as a way of defining and implementing enterprise applications that deals with the intercommunication of loosely coupled, coarse grained (business level), reusable artifacts (services). In this paper, we attempt to mathematically model the preliminary steps in the larger problem of providing an optimal architecture. The problem is treated as a complex network, particularly a process-task-network. We employ statistical and graph-theoretic methods namely, Jaccard's distance analysis, Multiple Correspondence method and the Minimum Spanning Tree method, to find appropriate clusters. These methods are used to cluster tasks across business processes to propose services. Additional properties and features of these clusters are discussed. We propose a leverage factor which demonstrates the importance of a task within the service and its impact on service composition.