This paper introduces a technique to analyze and visualize social networks using Shannon's entropy model. Entropy is exploited to measure the information amount in social network graphs, and to conduct sensitivity analyses. Novel measures such as degree, betweenness and closeness entropies are evaluated to find the change in graph entropy or the actors. In this work we present a visualization approach that uses coloring, sizing and filtering to help the users perceive the communicated information. The result of sensitivity analyses is integrated into the visualization using the change amount caused by the actors as information. The main contribution of this study is a visualization where the information communicated from a social network is enhanced by the help of sensitivity analyses.