## 4 Analysis and Findings
### A Multivariate Statistical Approach  
To develop a procedure for briefly grouping together accounts that share followers, we introduce the use of a similarity measure suitable for this kind of representation. The problem with choosing a similarity measure for Twitter accounts is that there is a great diversity of the number of followers of the accounts. Accounts are not comparable for this reason. A correlation coefficient is not an adequate \begin{table}
\begin{tabular}{c l l l l l l l} \hline \hline
**Category** & **Accounts** & **Min** & **Q\({}_{1}\)** & **M** & **Q\({}_{3}\)** & **Max** &
\begin{tabular}{l} **Mean number of followers** \\ **(SD)** \\ \end{tabular} \\ \hline \multirow{4}{*}{1} & HCoastGuard, Diavgeia, & & & & & & & \\  & GGNeasGenias, Govgr, & & & & & & \\  & Hellenicpolice, MinDevGR, & & & & & & \\  & GreeceMFA, Yyka\_gov, & & & & & & \\  & YPEKA, OpenGovGr, & & & & & & \\  & Pyrosvestiki, PrimeministGR, & & & & & & \\  & Synigoros, VisitGreecegr & & & & & & \\ \hline
2 & Yp\_Paideias, StartupGreece & 2 & 6 & 7 & 8 & 13 & 3,910 (3,005) \\ \hline
3 & DigiPlanGR & 2 & 6 & 7 & 8 & 12 & 738 \\ \hline
4 & Gsis\_gov\_gr, PressParliament & 2 & 5 & 6 & 7 & 11 & 621 (159) \\ \hline
5 & Digitalgreece & 2 & 5 & 6 & 7 & 10 & 469 \\ \hline
6 & GGMEofficial & 2 & 2.75 & 3 & 4 & 5 & 76 \\ \hline
7 & e\_ekpaideusi & 2 & 2 & 2 & 3 & 3 & 77 \\ \hline
8 & Synigkatanaloti & 2 & 2 & 2 & 2 & 2 & 38 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The eight distribution categories of e-government Twitter accounts according to the number of combinations to which the accounts belong. measure, because it considers both the unities and the zeros. The idea that we use in the present paper is that two accounts should be comparable despite their relative sizes, and only the unities should be counted. Therefore, when comparing two accounts, we considered the size of the smaller account and measure how many of its followers also follow the larger account. In Table 3, we present an example of how to elaborate on a suitable similarity coefficient [60]. Suppose there are two Twitter accounts, A and B. Then, suppose that these two accounts have \(a\) followers in common. Table 3 shows that besides those \(a\) followers, there are also \(b\) followers that follow B, but not A and \(c\) followers that follow A, but not B, and of course, there are those followers (\(d\)), who follow none of the two. The Simpson similarity coefficient \(S\) is defined as [60]:  
\[S=\frac{a}{\min\ (a+b,a+c)}\]  
\(S\) equals the number of common followers divided by the number of followers of the account that has the fewest followers. For example, Simpson similarity for the Hellenic police and Coast Guard accounts equals 0.774, because 77.4% of the followers of the Coast Guard account (1178 of 1522 followers) also follow the Hellenic police account (which has 31,423 followers in total). A 27 by 27 symmetric Simpson similarities matrix is then constructed. This matrix serves as the input data in a multidimensional scaling procedure (MDS) [61]. This multivariate statistical procedure transforms original similarities into new ones in a space of fewer dimensions, in order to reduce the dimensionality. A goodness-of-fit index, named \"stress\" is used in order to decide whether the method reproduces the original similarities adequately. Stress is a loss function in this context, which is minimized using a procedure called \"stress majorization\". Stress is a measure of the goodness-of-fit between the distances of the original data and the distances of the reproduced data. It measures the squared differences between ideal (low-dimensional) distances and actual distances in the high-dimensional space [59]. Small values of stress (lower than 0.05) indicate a good fit and representation of the original data to the new lower dimensional space. To achieve this value of stress, a reduction to four dimensions is made using the Simpson similarity matrix (Stress = 0.034). Therefore, for every account, four coordinates could now be used.