# Email Based Institutional Network Analysis: Applications and Risks

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## Abstract

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## 1. Introduction

- Suitable indicators that take into account the direction, intensity and frequency of information flow among the organisation’s members.
- How such indicators can be connected with human resources and the overall organisation efficiency measurement.
- What are the possible areas of application and the trade-offs when applying such an approach?

## 2. Research on Emails and Organizational Dynamics

## 3. Description of the Dataset

## 4. Modelling Based on Social Network Analysis Indicators

- ${\tau}_{i}$ is the number of triangles formed between node i and its possible neighbours.
- ${d}_{i}$ is the degree of the node (the number of individual connections).

- Middleperson: a triangle where the two arcs of i have different directions and there is an arc between j and k (or vice versa), without forming a cycle. There are two arcs incoming to k or j (j→i, i→k, j→k or vice versa) (Figure 2d)

^{2}is remarkably high at 0.8781. The number of emails sent from i to j appears to be positively correlated with the out-closeness centrality of i—i.e., how close i is to the centre of the network as regards sending emails. Nevertheless, it is negatively correlated with the in-closeness centrality of i. Seen from the j point of view, the in- and out-closeness centrality estimates have—as expected—the opposite signs. The correlation with the local clustering coefficient is not as straightforward. The in-, out- and middleperson indicators of i show a positive correlation, while the cycle clustering coefficient has a negative correlation. On the side of j, the correlations are not symmetrical. It may be implied that the middleperson role generates more email activity, while the cycle role generates less, for both i and j. It is also interesting to note that the strength of email exchanges is expected to be higher when i and j belong to the same department.

^{2}is lower (0.5556), but still acceptable. Most probably, the influence of possible weekends between the original email and its reply distorts the results. Even so, the estimates for the independent variable are in the expected direction. Individuals with high out-closeness centrality are expected to reply (as j) and be replied to (as i) faster than the average, while high in-closeness has the opposite effect. The in- and out-clustering coefficients have opposite signs, but have the same direction for i and j. This suggests that individuals with a high out-clustering indicator reply and are replied to faster. High in-clustering or cycling clustering coefficients suggest higher delays in replies. The middleperson clustering coefficient has a negative time for i and a positive one for j. Finally, similarly to the case of intensity, the time to reply is, on average, lower when i and j belong to the same department.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Disclaimer

## References

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**Figure 1.**Total number of emails sent and received by each department (bubble size equals number of department members).

Department | Members | Sent | Received | Sent Per Member | Received Per Member |
---|---|---|---|---|---|

D_4 | 109 | 38,614 | 39,693 | 354 | 364 |

D_14 | 92 | 31,747 | 34,298 | 345 | 373 |

D_1 | 65 | 27,829 | 23,234 | 428 | 357 |

D_21 | 61 | 23,195 | 21,528 | 380 | 353 |

D_22 | 25 | 18,906 | 7501 | 756 | 300 |

D_15 | 55 | 18,437 | 17,905 | 335 | 326 |

D_0 | 49 | 17,075 | 18,477 | 348 | 377 |

D_7 | 51 | 15,108 | 17,018 | 296 | 334 |

D_17 | 35 | 13,077 | 11,995 | 374 | 343 |

D_13 | 26 | 12,800 | 10,464 | 492 | 402 |

id | Sent | Received | Department |
---|---|---|---|

987 | 9782 | 789 | D_22 |

629 | 6585 | 2843 | D_1 |

178 | 5939 | 1684 | D_0 |

168 | 5664 | 4710 | D_4 |

586 | 5106 | 2810 | D_21 |

356 | 4905 | 2723 | D_8 |

98 | 4531 | 1416 | D_16 |

746 | 4153 | 1472 | D_15 |

288 | 3806 | 484 | D_37 |

316 | 3768 | 1722 | D_1 |

id | Sent | Received | Department |
---|---|---|---|

168 | 5664 | 4710 | D_4 |

912 | 3590 | 3223 | D_14 |

947 | 2243 | 3042 | D_7 |

629 | 6585 | 2843 | D_1 |

586 | 5106 | 2810 | D_21 |

356 | 4905 | 2723 | D_8 |

472 | 1550 | 2717 | D_6 |

915 | 3705 | 2513 | D_11 |

891 | 2069 | 2305 | D_38 |

416 | 2100 | 2302 | D_9 |

Intensity of Bilateral Emails $\mathbf{log}({\mathit{w}}_{\mathit{i}\mathit{j}})$ | Time for Email to Be Replied to $\mathbf{log}({\mathit{t}}_{\mathit{j}\mathit{i}})$ | |||||
---|---|---|---|---|---|---|

Independent Variable | Estimate | Level of Significance Pr(>|t|) | Estimate | Level of Significance Pr(>|t|) | ||

${C}_{i}^{\text{}closeness,in}$ | −4.70199 | <2 × 10^{16} | *** | 6.803725 | <2 × 10^{16} | *** |

${C}_{i}^{\text{}closeness,out}$ | 8.127924 | <2 × 10^{16} | *** | −6.31347 | <2 × 10^{16} | *** |

${C}_{i}^{in}$ | 0.572814 | <2 × 10^{16} | *** | 1.258198 | <2 × 10^{16} | *** |

${C}_{i}^{out}$ | 0.434099 | <2 × 10^{16} | *** | −0.55758 | <2 × 10^{16} | *** |

${C}_{i}^{middleperson}$ | 1.225002 | <2 × 10^{16} | *** | −2.5339 | <2 × 10^{16} | *** |

${C}_{i}^{cycle}$ | −2.37641 | <2 × 10^{16} | *** | 1.35217 | <2 × 10^{16} | *** |

${C}_{j}^{\text{}closeness,in}$ | 7.661745 | <2 × 10^{16} | *** | 15.34833 | <2 × 10^{16} | *** |

${C}_{j}^{\text{}closeness,out}$ | −9.46001 | <2 × 10^{16} | *** | −10.6287 | <2 × 10^{16} | *** |

${C}_{j}^{in}$ | −1.55559 | <2 × 10^{16} | *** | 0.38119 | <2 × 10^{16} | *** |

${C}_{j}^{out}$ | −0.83673 | <2 × 10^{16} | *** | −0.86216 | <2 × 10^{16} | *** |

${C}_{j}^{middleperson}$ | 3.620311 | <2 × 10^{16} | *** | 0.375042 | 1.63 × 10^{11} | *** |

${C}_{j}^{cycle}$ | −1.15051 | <2 × 10^{16} | *** | 0.193783 | 0.00147 | ** |

$Dep{t}_{i}=Dep{t}_{j}$ | 0.051719 | <2 × 10^{16} | *** | −0.18322 | <2 × 10^{16} | *** |

Adjusted R-squared | 0.8781 | 0.5556 | ||||

p-value | <2.2 × 10^{16} | <2.2 × 10^{16} |

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Christidis, P.; Gomez Losada, Á.
Email Based Institutional Network Analysis: Applications and Risks. *Soc. Sci.* **2019**, *8*, 306.
https://doi.org/10.3390/socsci8110306

**AMA Style**

Christidis P, Gomez Losada Á.
Email Based Institutional Network Analysis: Applications and Risks. *Social Sciences*. 2019; 8(11):306.
https://doi.org/10.3390/socsci8110306

**Chicago/Turabian Style**

Christidis, Panayotis, and Álvaro Gomez Losada.
2019. "Email Based Institutional Network Analysis: Applications and Risks" *Social Sciences* 8, no. 11: 306.
https://doi.org/10.3390/socsci8110306