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The social networks are widely used by millions of people worldwide. The trust concept is one of the most important issues in Social Network Analysis (SNA) which highly affects the quantity and quality of the inter-connections, decisions, and interactions among the users in e-commerce or recommendation systems. Many normative algorithms are developed to calculate the trust which most of them are complicated, depend on the network structure, and need lots of critical information that makes them hard to use. The aim of this paper is proposing a descriptive, simple and effective method for calculating the maximal trust and the trust route between any two users of an Online Social Network (OSN). For this purpose, four new models for estimating the trust mechanism of the users are proposed and analyzed using Kolmogorov–Smirnov and Anderson–Darling statistical hypothesis tests to identify and validate the best-fitted model based on 20,613 empirical results gathered from 4552 social network volunteers. Due to the time–complexity of the problem, a meta-heuristic algorithm based on the Artificial Bee Colony (ABC) optimization method is also developed for solving the best-fitted model. The proposed algorithm is simulated in Matlab® over six larger test cases adopted from the Facebook dataset. In order to evaluate the performance of the developed algorithm, the Ant Colony Optimization (ACO) and Genetic Algorithm (GA) based meta-heuristics are also simulated on the same test cases. The comparison of the computational results shows that the ABC approach performs better than the ACO and GA as the size of the network increases. [ABSTRACT FROM AUTHOR]