Measuring influence, through centrality measures, has been a center-piece of research in the analysis of complex social networks, such as finding coherent communities (clusters) and locating trend setters (prototypes) in viral marketing. Even though there exists a few axiomatic frameworks associated with some specific forms of influence measures in the literature, these formal frameworks are not generic in nature in terms of characterizing the space of influence measures for complex social networks. To address this research gap, we propose a generic axiomatic framework, in this paper, to capture most of the key intrinsic properties of any influence measure in networks. We further analyze certain popular centrality measures using this framework. Interestingly, our analysis reveals that none of the centrality measures considered satisfies all the desirable axioms. We finally conclude this paper by stating an appealing conjecture on a potential impossibility theorem associated with the proposed axiomatic framework.