Degree Distributions in Ibāḍī Prosopographies | توزيع الروابط في البروسوبوغرافيات الإباضية

Lately, I have been working on applying network analysis to some of the data taken from Ibāḍī prosopographical works. This post shows the results of one of the five books I have been working on, the Siyar al-Wisyānī, a composite text compiled over the 11th and 12th centuries. The graph is what is called a "degree distribution" in network analysis, and visualizes the connections among Ibāḍī scholars in the texts. A 'degree' refers to the number of edges (or 'links') any given node in the network has with other nodes. Here, the nodes are Ibāḍī scholars. The remarkable feature of this text is the entirely uneven distribution of edges: a handful of scholars have much higher degrees than the average. This means that the Siyar al-Wisyānī exhibits the same structure of other 'real-world' networks (whether they be among people, diseases, or computers). This phenomenon, called the 'power-law distribution' means that this handful of individuals are responsible for linking most other nodes in the network together. The resulting effect is often called the 'small world' effect in which the path between any two nodes in the network is actually remarkably short. In this case, the average path between any two Ibāḍī scholars is less than 4...remarkable given that the network consists of nearly 200 scholars.

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Figure 1: This chart shows that the Siyar al-Wisyānī exhibits a 'power-law' degree distribution. This means that a handful of Ibāḍī scholars in the text who have unusually high degrees are responsible for most connections between other scholars.