## 4 Analysis and Findings
### An Association Rules Approach
Figure 3 describes the ability of the accounts to share followers and form combinations with other accounts that share followers with them. In Figure 3, if a combination of 13 accounts is included in the rightmost bar, then part of this combination (having 12 accounts) is also included and presented in the second last bar. The left bars describe combinations with fewer members than those described by bars on the right and probably some additional new combinations. For a combination of k member accounts, all the combinations with fewer member accounts are also included and presented in the graph. It is interesting that when moving from combinations of 13 members to combinations of seven members, the number of combinations increases: 15-185-...-16,746, while the number decreases when moving from combinations of seven members to combinations of one member. The mode of this distribution is seven, which means that it is very likely to find combinations of seven accounts that share followers. The mean equals seven and the standard deviation equals 1.7. Therefore, on average, there will be combinations of seven accounts, and also, combinations ranging from five to nine accounts are frequent. By raising support (and confidence), we can limit both the number and size of combinations and arrive at combinations of accounts that share more followers. Figure 4 presents the average number of followers for every combination size. The graph presents average numbers of followers counted for combinations of accounts at each step of the procedure. Followers that follow small combinations can also follow combinations of more accounts. Combinations of five to nine accounts that share followers have an average number of shared followers that ranges from 94 to 35. Only combinations of up to four accounts have an average number of shared followers that is greater than 100, and only combinations of two accounts have an average of more than 1000 shared followers. In Figure 5, we present eight box-plots. Box-plots are constructed using minimum and maximum values and the median, M, 25% percentile (Q\({}_{1}\)) and the 75% percentile (Q\({}_{3}\)). To construct the box-plots, we considered all the observations reported in Figure 3, that is a total of 72,586 cases. Additionally, we considered for every Twitter account how many times it belongs to a combination of two, three, four, and so on, accounts. Then, we constructed 27 box-plots, one for each account. Each box-plot represents the distribution of the number of combinations to which a specific account belongs. Because many such box-plots are the same for several accounts, for economy, we grouped together accounts having the same box-plots. Eight distribution categories are formed. In Figure 5, the eight  
Figure 3: Distribution of combinations of accounts that share followers. categories are presented along with their associated box-plots. Box-plots are presented in descending order: from distributions of accounts that can have members in combinations of up to 13 members, to distributions of accounts that have members in combinations of fewer members. A description of the distribution categories is presented in Table 2.  
Figure 4: Average number of followers for every combination size. Figure 5: Box-plots of Twitter accounts regarding their membership in combinations of accounts sharing followers. In Table 2, it can be seen that in Category 1, accounts may be members of combinations of up to 13 accounts. That is, they may have common followers with up to 12 other accounts. Accounts in Categories 1 to 3 and, to a smaller degree, accounts in Categories 4 and 5 share followers with many other accounts. It is interesting that the majority of the accounts and all the accounts of the Ministries share followers with many accounts, since they belong in Categories 1 to 3. The accounts, GGMEofficial, E_ekpaideusi and Synigkatanaloti, are isolated.