Trophic analysis of a historical network reveals temporal information

Abstract

Trophic analysis exposes the underlying hierarchies present in large complex systems. This allows one to use data to diagnose the sources, propagation paths, and basins of influence of shocks or information among variables or agents, which may be utilised to analyse dynamics in social, economic and historical data sets. Often, the analysis of static networks provides an aggregated picture of a dynamical process and explicit temporal information is typically missing or incomplete. Yet, for many networks, particularly historical ones, temporal information is often implicit, for example in the direction of edges in a network. In this paper, we show that the application of trophic analysis allows one to use the network structure to infer temporal information. We demonstrate this on a sociohistorical network derived from the study of hadith, which are narratives about the Prophet Muhammad’s actions and sayings that cite the people that transmitted the narratives from one generation to the next before they were systematically written down. We corroborate the results of the trophic analysis with a partially specified time labelling of a subset of the transmitters. The results correlate in a manner consistent with an observed history of information transmission flowing through the network. Thus, we show that one may reconstruct a temporal structure for a complex network in which information diffuses from one agent to another via social links and thus allows for the reconstruction of an event based temporal network from an aggregated static snapshot. Our paper demonstrates the utility of trophic analysis in revealing novel information from hierarchical structure, thus showing its potential for probing complex systems, particularly those with an inherent asymmetry.

Influence and influenceability: global directionality in directed complex networks

“…Trophic analysis is a technique to quantify the global directionality inherent in real directed networks [5], and is applicable to any directed network. Trophic analysis was originally derived from ecology [17] where the original definition linked hierarchy to weighted steps from the basal nodes (vertices of in-degree zero), which is an intuitive way to view hierarchy but cannot be generalized to any directed network without basal nodes like the definition used here and in [5][6][7]18]. Much of the previous work which applied trophic level and incoherence used the previous definition [14,17,[19][20][21].…”