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We have developed a search method that uses both hyperlinks and social links and thus combines the merits of searching and social communication. A user can quickly search for not only web pages but also for other users currently accessing those pages ("real-time users"). Each URL on the search engine results page is annotated with the number of real-time users. On each page linked from the search engine results page, each hyperlink is annotated with the number of real-time users. By using these links, a user can communicate with other real-time users who may have more knowledge about the topic of the linked page. All linked pages provide a window for sending queries in real time and for communicating with other real-time users. The window also shows a log of previous communications through that page, enabling a user to see if a similar query was previously sent and answered, which would obviate the need to send it again. Furthermore, users can highlight text on a linked page, enabling other users to quickly find important information as the system can automatically scroll down and present the highlighted text after the linked page is accessed. We have also developed a page ranking algorithm based on a hyperlink structure and a social network structure. The social network structure reflects the "quality" and number of real-time users. A user can thus access the most popular web pages and experts in real time. In our ranking algorithm, how to timely reflect real-time user activities becomes a key point for our system validity. In this paper, we especially focus on it. As a first phase, in order to shorten the calculation time of our ranking method, we investigated SLEPc, a parallel computing library based on Open MPI and PETSc. We evaluated three calculation methods, Lanzcos, Arnoldi and Krylov-Schur, implemented in SLEPC. As a result, we confirmed that we can complete the eigenvalue and the eigenvector calculation of a probability transition matrix with hundreds of t- - housands rows and columns in dozens of seconds. Based on the investigation of this paper, we will implement our ranking algorithm on the prototype system.