## 7 Use-Case Analysis
### Knowledge Sharing: Are There Role/Gender Barriers? An important aspect of co-workers interaction is homophily, defined as the tendency of individuals to associate and link with similar others. Several studies on the effect of homophily in interpersonal relations (e.g., References [30,57]) confirmed that homophily can also become a barrier to effective knowledge sharing, when strongly homophily-oriented individuals are not exposed to external stimuli and new experiences. In fact, while facilitating coordinated action by managers, homophily may adversely restrict decision-making options [13]. In the section, we investigate homophily by role and gender. First, we introduce a model of homophily. Since, in a thread-based model, authors post a message without specifying the addressee, only the action of commenting a message may, or may not, be influenced by the gender of the author. Therefore, denoting with \(g\) (\(=\)_male_, \(female\)) the gender to which a user \(x\) belongs, we model the \(g\)-_homophily_ as the conditioned probability that a \(g\) commenter answers a \(g\) author:  
\[P(g\text{-}\textit{commenter}|g\text{-}\textit{author})=\frac{P(g\text{-} \textit{commenter}\cup g\text{-}\textit{author})}{P(g\text{-}\textit{author})}. \tag{13}\]  
In case of statistical independence, we have:  
\[ \begin{gathered}\frac{P(g\text{-}\textit{commenter}\cup g\text{ -}\textit{author})}{P(g\text{-}\textit{author})}=\\ \frac{P(g\text{-}\textit{commenter})\times P(g\text{-}\textit{ author})}{P(g\text{-}\textit{author})}=P(g\text{-}\textit{commenter})\.\end{gathered}  \tag{14}\]  
Accordingly, we state our homophily hypotheses as follows:  
**Hypothesis 1**. : _(neutrality): There is no statistically significant difference between the probability that a \(g\)-commenter answers a \(g\)-author and the prior probability of \(g\)-commenters._  
**Hypothesis 2**. : _(homophily): The probability that a \(g\)-commenter answers a \(g\)-author is significantly higher than the prior probability of \(g\)-commenters._To test our hypotheses we divide the three-year dataset into 3-month slots, and, in each slot, we estimate \(P(g\text{-}\textit{commenter}\cup g\text{-}\textit{author})\) as the number of messages posted by a g-commenter in answer to a g-author (purging additional comments posted by the author itself), while \(P(g\text{-}\textit{author})\) and \(P(g\text{-}\textit{commenter})\) are estimated by the number of such messages addressed to a g-authors or originated by a g-commenter, respectively. Next, we apply the Wilcoxon signed-rank test ([[https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test](https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test)]([https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test](https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test)), accessed on 1 September 2021), which is a paired difference test. Since the Wilcoxon test implies counting the number of times the difference between pairs is positive or negative, without considering the amount of the difference, we also compute a z-test over the full period to rank significant results (according to the Wilcoxon) as highly or moderately significant. Figure 7 plots prior and conditional probabilities and shows that both males and females are homophilous (according to Wilcoxon test); however, females are considerably more homophilous than males according to the z-test: in fact, for females, Hypothesis 2 is accepted with \(p=7.12\times 10^{-8}\), while, for males, we obtain \(p=0.02111\) (hence, \(p\geq 0.01\)). These results are in contrast with References [30; 31], who did not detect substantial women homophily; however, their experiments were conducted on friendship networks, representing a less formal environment than an ESN. A homophily result similar to ours was instead obtained in Reference [28] with reference to an online combat game: this type of social network is more similar to an ESN than to a friendship network, since relationships are established according to confidence and competence, rather than socialization needs.