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Prestigious members on social networking websites are attracting increasing attentions from peers and corporations. People are used to consulting prestigious members for useful information and corporations are seeking opportunities to leverage them for ''word of mouth'' advertising. Identification and recognition of these prestigious members have been a crucial issue. Besides, the dynamic nature of members' behaviour determines the evolving nature of members' prestige. With the evolution of members' behaviour, currently prestigious members may be substituted by others who are not prestigious at present. The prediction of members' prestige evolution will help discover potential prestigious members, which will then help both people and corporations move to secure their long-term interests. However, little work has been done in relation to prediction of prestigious members. This paper aims to fill this gap specially using Flickr groups as a testbed. By investigating social actions among members, a graph-based action network framework to predict evolution of prestigious members has been proposed. Based on the social structural theory, which points out the interactive effect between social structure and users' actions, a favor action network that captures the social actions of choosing favourite photos of members is constructed. According to the network theory, properties of the nodes in the favor action network are investigated to identify currently prestigious members, and structural properties underlying the favor action network are mined to analyze the communication behaviour of members in a group. Further, the sociological theory inspires four key factors that affect members' favor action intentions, which are homophily, triadic interaction rule, continuity and recency. Based on the above analysis, a hybrid algorithm taking all these four factors into account is proposed to predict members' prestige evolution. Finally, several comprehensive and systematic analyses are designed and conducted to evaluate each of the functional components of the proposed framework. Results of evaluation on a real-world dataset validate its performance.