In February 2012, Kobe Bryant, the American basketball star, joined Chinese microblogging site Sina Weibo. Within a few hours, more than 100,000 followers joined his page, anxiously waiting for his first microblogging post on the site. The media considered the tremendous number of followers Kobe Bryant received as an indication of his popularity in China. In this case, the number of followers measured Bryant's popularity among Chinese social media users. In social media, we often face similar tasks in which measuring different structural properties of a social media network can help us better understand individuals embedded in it. Corresponding measures need to be designed for these tasks. This chapter discusses measures for social media networks.

When mining social media, a graph representation is often used. This graph shows friendships or user interactions in a social media network. Given this graph, some of the questions we aim to answer are as follows:

1. • Who are the central figures (influential individuals) in the network?

2. • What interaction patterns are common in friends?

3. • Who are the like-minded users and how can we find these similar individuals?

To answer these and similar questions, one first needs to define measures for quantifying centrality, level of interactions, and similarity, among other qualities. These measures take as input a graph representation of a social interaction, such as friendships (adjacency matrix), from which the measure value is computed.