Analysing the Network of Narrators

To analyse our network of narrators, we can look to structure the network formed by the narrators in Bukhari’s collection, and then see how the structure varies for narrators. One can expect to find groups of narrators that are ‘close-knitted’, or narrators that do not form part of any close-knit community.
Since we are analysing narrators from Bukhari’s collection, it is important to bear in mind that any structure identified therein may be an artifact of Bukhari’s criteria for selecting thiqa narrators.

Measures of Network Cohesion

There are some basic measures of network cohesion that can be used to acquire a higher level understanding of a network. The density of a graph is the ratio of the number of actual connections and the number of possible connections in a network. For our network, the density happens to be quite low: 0.003.
The reciprocity of a network measures the proportion of mutual connections in a network, where mutual connection refers to nodes reciprocating connections with each other. In our case, this would measure the extent to which nodes relate narrations from and to each other. Perhaps expectedly, this too is low in our network: 0.03.
The transitivity of a network measures the density of triangular connections in a network. This is 0.07 for our network.

In-Degree Network of Narrators

The chart below shows the network of narrators modelled as nodes, whilst sizing the nodes for number of in-degree connections with other nodes. In other words, a narrator has a larger sized node if it has received narrations from a high number of different narrators.

An interactive, unlabeled chart, is available here to let the user explore independently. Below, a static chart is available with some labelling for narrators with highest in-degree connections.

We can see that in our network, majority of nodes are grouped close to the centre. Although edges are not displayed in the chart above so as to not clutter it, we did not see any connections amongst nodes placed away from the populous centre.

A densely populated centre with edges/connections primarily amongst them means that a large amount of communication occurs only amongst the population at centre. This is expected, since Bukhari would have identified some narrators as trustworthy per his standards, to then include in his collection narrations conveyed exclusively by the aforesaid group.

In the chart presented above, nodes are sized based on their in-degree values — a narrator to whom a large number of other narrators narrate would feature with a larger size. We can see that in this case, most of large nodes consist of Tabi'een, Taba' Tabi'een, and then 3rd Century Narrators.

Out-Degree Network of Narrators

The out-degree measure refers to the number of communications or links going out from a narrator to other narrators. Nodes are sized based on the number of narrators they convey narrations to.

An interactive version of the chart is available here. A static version is presented below.

We now see that Companions, Tabi'een, and Taba' Tabi'een appear to be those with higher our-degree values. In simpler terms, this means that narrators from the aforesaid categories transmitted ahadith to others in large numbers, and could be viewed as instrumental in spreading ahadith.

Eigen Centrality of Narrators

Generally, the Eigenvector Centrality measures how central a narrator is to the entire network. This is done by scoring narrators on how many narrators they are connected to, and in turn, how many narrators these narrators connect to, in the entire network. Whilst the Degree Centrality measures local importance (that is, limited to the particular narrator), Eigenvector Centrality is able to measure global importance.

An interactive version is available here; a static version follows.

Between-ness Centrality of Narrators

The Between-ness centrality measures how much a narrator is ‘in between’ other narrators, or the number of shortest paths to a particular narrator.

An interactive version of the chart above can be accessed here. Companions and Tabi'een are noticeably important. In particular, we can see al-Zuhri from the Tabi'een as having the highest between-ness score, whilst from Companions, the highest score was for Abu Hurairah.

In the next post, we shall be looking to identify structure/groups in our network

A Statistical Study of Al Bukhari’s Hadith Collection

Part 2