The increasing popularity of virtual computing environments such as Cloud and Grid computing is helping to drive the realization of ubiquitous and pervasive computing. However, as computing becomes more entrenched in everyday life, the concepts of trust and risk become increasingly important. In this paper, we propose a new graph-based theoretical approach to address trust and reputation in complex ubiquitous networks. We formulate trust as a function of quality of a task and time required to authenticate agent-to-agent relationship based on the Zero-Common Knowledge (ZCK) authentication scheme. This initial representation applies a graph theory concept, accompanied by a mathematical formulation of trust metrics. The approach we propose increases awareness and trustworthiness to agents based on the values estimated for each requested task, we conclude by stating our plans for future work in this area.
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