Modeling and naming general entity-entity relationships is challenging in construction of social networks. Given a seed denoting a person name, we utilize Google search engine, NER (Named Entity Recognizer) parser, and CODC (Co-Occurrence Double Check) formula to construct an evolving social network. For each entity pair in the network, we try to label their categories and relationships. Firstly, we utilize an open directory project (ODP) resource, which is the largest human-edited directory of the web, to build a directed graph, and then use three ranking algorithms, PageRank, HITS, and a Markov chain random process to extract potential categories defined in the ODP. These categories capture the major contexts of the designated named entities. Finally, we combine the ranks of these categories and tf*idf scores of noun phrases to extract relationships. In our experiments, total 6 evolving social networks with 618 pairs of named entities demonstrate that the Markov chain random process is better than the other two algorithms.