Topic-specific TwitterRank

the influence of a twitterer can be interpreted similar to the “authority” of a web page: a twitterer has high influence if the sum of influence of her followers is high; at the same time, her influence on each follower is determined by the relative amount of content the follower received from her.
There are major differences between authority and influence. The influence on each follower is purely based on relative amount of content the follower receives as the latter may not read content with topics less interesting even when the relative content is large. Since twitterers generally have different expertise and/or interests in various topics, influence of twitterers also vary in different topics.

Twitterer network:
A directed graph D(V,E) is formed with the twitterers and the “following” relationships among them. V is the vertex set, which contains all the twitterers. E is the edge set. There is an edge between two twitterers if there is “following” relationship between them, and the edge is directed from follower to friend.

A topic-specific random walk model is applied to calculate the user’s influential score. The transition matrix for topic t, denoted as P_t. The transition probability of surfer from follower s_i to friend s_j is: Topic-specific teleportation: The influence scores of twitters are calculated iteratively: Aggregation of topic-specific TwitterRank:

• WENG, J., LIM, E.-P., JIANG, J. & HE, Q. 2010. TwitterRank: finding topic-sensitive influential twitterers. Proceedings of the third ACM international conference on Web search and data mining. New York, New York, USA: ACM.