Twitter is one of the most popular social network services (SNS) applications, in which users can casually post their messages. Given that users can easily post what they feel, Twitter is widely used as a platform to express emotions. These emotional expressions are considered to possibly influence user relationships on Twitter. In our previous study, we analyzed this influence using emotional word dictionaries. However, we could not measure the emotion scores for the words not included in the dictionaries. To solve this problem, in this study, we use the Naive Bayes and consider dependency parsing, i.e., the structure of tweets and the relationships of words. Furthermore, we introduce a set of new measures, namely total positive emotion score (TPES), total negative emotion score (TNES), and total neutral emotion score (TNtES). Based on these measures, we define a new composite index (CI) for emotion scores, which is a normalized value in the range of 0 to 1. We categorize users into positive and negative groups based on the composite index and test the difference of user relationships between these two groups with a statistical method. The result demonstrates that the relationships of positive users not only get better (i.e., the number increases) with time, but also tends to be mutual, which is consistent with the result of our previous study.