Rumor Diffusion within Organisations (817 Words)
A Social Network Analysis on the SG&R Law Firm Using Diffusion Models
Mohammad Mohsen Mahdi Zadeh Naeini
Introduction
Informal news diffusion in organizations has positive and negative consequences. It affects productivity but enhances familiarity with organizational norms. Thus, managers must understand the diffusion process to impede negative aspects and promote positive dissemination. This research primarily focuses on hindering news spread.
Theory
Grosser et al. (2010) posit that negative news diffusion relies on two factors: Shared connections between nodes, and Trust. Here, the first factor is measured by Node Redundancy and the second by Thresholds.
Data
The study uses network data from SG&R law firm (1988-1991), comprising a one-mode network with 34 partners across three offices (Lazega, 2001). It contains the following nodal attributes: gender, age, tenure years, practice, and law school.
Diffusion Models
The first model is a simple SI Model. I selected 1, 4, 8, 12, and 16 random nodes as seeds, depicting scenarios where up to approximately 50% of employees convey rumors. The subsequent plot illustrates seed numbers ascending from 1 to 16.
Regardless of seed count, in each scenario, all nodes become infected after about 10 steps. The networks significant embeddedness (14.26) enabled complete diffusion. To introduce control mechanisms, thresholds were incorporated; for each seeding, they incrementally rose to a minimum value that ensured spread containment.
Minimum thresholds for each seeding strategy are compiled below:
| 1 | 4 | 8 | 12 | 16 |
|---|---|---|---|---|
| 2 | 5 | 6 | 8 | 9 |
Excluding the scenario with one seed node, in the remaining 4 cases, company trust must be so low that, on average, each employee hears news from at least 53% of their neighbours to believe it. In the last scenario, even with the average neighbours as the threshold, the spread isnt contained. To test an alternative strategy, the recovery factor was added to the original five models, starting with 0.01 and increasing to 0.02 and 0.04.
In all scenarios, a recovery rate of 0.04 eventually results in more recovered than infected.
The recovery factor represents forgetting news. Recognizing that people dont typically forget permanently, a waning factor of 0.05 was introduced in the next model. A waning value of 0.05 implies nodes remember forgotten news after 20 steps, the maximum needed to contain news spread in the previous model.
In every seeding scenario, a recovery rate of 0.08 led recovered to exceed infected after approximately 19 steps.
Lastly, trust (thresholds), forgetting (recovery), and remembering (waning) factors are integrated. Waning rate remains constant (0.05), while threshold and recovery rate rise for containment. Plots depict containment conditions with 1 to 16 seed nodes.
Table contains thresholds and recovery rates ensuring diffusion containment for each seeding:
| 1 | 4 | 8 | 12 | 16 | |
|---|---|---|---|---|---|
| Threshold | 2 | 3 | 4 | 4 | 4 |
| Recovery Rate | 0.01 | 0.02 | 0.04 | 0.04 | 0.04 |
Diffusion in the Altered Network
This section delves into altering the network to hinder rumor diffusion.
Removing the Nodes with Degree Higher than Q3
As discussed, node embeddedness facilitates diffusion. Removing nodes with degree centrality and betweenness centrality exceeding a threshold should simplify containment. This section concentrates on degree centrality.
The Q3 of degree centrality is around 0.27. Eliminating nodes exceeding this value retains 75% of nodes while reducing redundancy from 14.27 to 3.96.
