In large social networks, nodes (users, entities) are influenced by others for various reasons. For example, the colleagues have strong influence on one's work, while the friends have strong influence on one's daily life. How to differentiate the social influences from different angles(topics)? How to quantify the strength of those social influences? How to estimate the model on real large networks? To address these fundamental questions, we propose Topical Affinity Propagation (TAP) to model the topic-level social influence on large networks. In particular, TAP can take results of any topic modeling and the existing network structure to perform topic-level influence propagation. With the help of the influence analysis, we present several important applications on real data sets such as 1) what are the representative nodes on a given topic? 2) how to identify the social influences of neighboring nodes on a particular node? To scale to real large networks, TAP is designed with efficient distributed learning algorithms that is implemented and tested under the Map-Reduce framework. We further present the common characteristics of distributed learning algorithms for Map-Reduce. Finally, we demonstrate the effectiveness and efficiency of TAP on real large data sets.