Perception, prestige and PageRank

Abstract

Academic prestige is difficult to quantify in objective terms. Network theory offers the opportunity to use a mathematical formalism to model both the prestige associated with an academic and the relationships between academic colleagues. Early attempts using this line of reasoning have focused on intellectual genealogy as constituted by supervisor student networks. The process of examination is critical in many areas of study but has not played a part in existing models. A network theoretical "social" model is proposed as a tool to explore and understand the dynamics of prestige in the academic hierarchy. It is observed that such a model naturally gives rise to the idea that the prestige associated with a node in the graph (the prestige of an individual academic) can be viewed as a dynamic quantity that evolves with time based on both local and non-local changes in the properties in the network. The toy model studied here includes both supervisor-student and examiner-student relationships. This gives an insight into some of the key features of academic genealogies and naturally leads to a proposed model for "prestige propagation" on academic networks. This propagation is not solely directed forward in time (from teacher to progeny) but sometimes also flows in the other direction. As collaborators do well, this reflects well on those with whom they choose to collaborate and those that taught them. Furthermore, prestige as a quantity continues to be dynamic even after the end of a relationship or career. Given that time ordering of relationships on the network are implicit but that measures such as betweenness are independent of this implicit time dependence: the success of a PhD student later in their career can improve the prestige of their doctoral supervisor. Thus, prestige can be interpreted to have dynamics that flow both forward and backward in time.

Fig 1. Simple model for academic hierarchy involving both supervisor-student links and examiner-examinee links.

Red lines represent examination relationships and blue lines represent supervisor/advisor relationships. In this diagram, A and B supervise E, who is examined by C and D; E then supervises G with D, who is in turn examined by A and F.

Fig 2. Simple closed loop showing the relationship where one examiner had the same intellectual "father" or "mother" as the supervisor of the student being examined.

Black lines show supervisory relationships. Red lines show examiner relationships.

Fig 3. Incestuous relationship loop, in which two supervisors who are children of the same intellectual parent, examine each other's students.

Black lines denote supervisory relationships. Red lines denote examiner relationships.

Fig 4. Supervisor / examiner relationships delayed by one generation.

Black lines denote supervisor relationships. Red lines denote examiner relationships.