Finding the Mule in the Network

There exist a variety of procedures for identifying clusters in large networks. This paper focuses on finding the connections between such clusters. We employ the concept of closed sets to reduce a network down to its fundamental cycles. These cycles begin to capture the global structure of the network by eliminating a great deal of the fine detail. Nevertheless, the reduced version is completely faithful to the original. No connection in the reduced version exists unless it was in the original network, connectivity is preserved. Reduction of as much as 80% can be observed in real networks. Just reducing the size makes comprehension of the network much easier.