Minimal Cover of Implication Rules to Represent Two Mode Networks

In a world full of connections between people and objects, new needs arise requiring multidisciplinary analysis of these new networks. This work presents a approach to analyze an Internet Service Provider (ISP) database using a minimal cover of implications extracted from formal concept analysis and complex network techniques. Our goal is to analyze access to the 25 most visited websites to find access patterns and its dependencies using a minimal cover of implications. 1,470,450 accesses carried out over a month were selected. The data were converted to a clarified formal context and the NextClosure algorithm was used to extract a minimal cover of implications. Implication rules were used to explore hidden substructures from the two mode networks. As a result, we found a set of 216 implications that explain every user access behavior. With a set of axioms we present the possibility of obtaining more specific rules by derivation. These implications represent access patterns that guarantee that whenever a set of websites are accessed, so is another set of websites. These results can aid in creating security policies and network configurations to help predict future accesses. Furthermore, with the implications we save a total of 99,90% of storage space needed to represent access behavior. Finally, we show that with the construction of the network based on implication rules, the relationships between the events (websites) of a two mode networks can be made.