A method computer implemented method of minimizing connections in a distributed system includes traversing paths in a directed graph representation of the distributed system having a fixed set of paths between nodes representing resources of the distributed system and edges representing connections between the resources by performing a random walk procedure to provide a reduced number of paths in the directed graph representation, and identifying excessive connections between the resources by simulating a client accessing the resources and identifying as excessive, connections that are not used by any of the reduced number of paths, wherein the excessive connections are removable from the distributed system without preventing client access to resources in the distributed system.