This exploratory study investigates the use of a computational knowledge engine (WolframAlpha) and social networking sites (Gmail, Yahoo and Facebook) by 200 students at De La Salle-College of Saint Benilde, their "friends" and their "friends of friends" during the 2009 through 2013 school years, and how this appears to have added value in knowledge generation. The primary aim is to identify what enhances productiveness in knowledge generation in Philippine Tertiary Education. The phenomenological approach is used, therefore there are no specific research questions or hypotheses proposed in this paper. Considering that knowledge generation is a complex phenomenon, a stochastic modelling approach is also used for the investigation that was developed specifically to study un-deterministic complex systems. A list of salient features for knowledge generation is presented as a result. In addition to these features, various problem types are identified from literature. These are then integrated to provide a proposed framework of inclusive (friendly) and innovative social networks, for knowledge generation in Philippine tertiary education. Such a framework is necessarily multidisciplinary and useful for problemsolving in a globalized and pluralist reality. The implementation of this framework is illustrated in the three parts of the study: Part 1: Online lessons, discussions, and examinations in General Psychology, Introduction to Sociology, and Life and Works of Jose Rizal, for the author's students in De La Salle-College of Saint Benilde; Part 2: Facebook Report analytics of students and teachers, their friends and their friends of friends via WolframAlpha; and Part 3: Social Network Analysis of the people and groups influencing the courses' scope-and-sequence in the new General Education Curriculum for Tertiary Schools and Institutions in the Philippines.