Universal Properties of Mythological Networks

As in statistical physics, the concept of universality plays an important, albeit qualitative, role in the field of comparative mythology. Here we apply statistical mechanical tools to analyse the networks underlying three iconic mythological narratives with a view to identifying common and distinguishing quantitative features. Of the three narratives, an Anglo-Saxon and a Greek text are mostly believed by antiquarians to be partly historically based while the third, an Irish epic, is often considered to be fictional. Here we use network analysis in an attempt to discriminate real from imaginary social networks and place mythological narratives on the spectrum between them. This suggests that the perceived artificiality of the Irish narrative can be traced back to anomalous features associated with six characters. Speculating that these are amalgams of several entities or proxies, renders the plausibility of the Irish text comparable to the others from a network-theoretic point of view. editor’s choice Copyright c © EPLA, 2012 Introduction. – Over the past decades many statistical physicists have turned their attention to other disciplines in attempts to understand how properties of complex systems emerge from the interactions between component parts in a non-trivial manner. Applications include the analysis of complex networks in the natural, social and technological sciences as well as in the humanities [1–5]. One of the notions intrinsic to statistical physics is universality, and attempts have been made to classify complex networks from a variety of areas to facilitate comparison amongst them [6,7]. Universality is also an important, albeit hitherto qualitative, notion in the field of comparative mythology. Campbell maintained that mythological narratives from a variety of cultures essentially share the same fundamental structure, called the monomyth [8]. Here we statistically compare networks underlying mythological narratives from three different cultures to each other as well as to real, imaginary and random networks. In this way we quantitatively explore universality in mythology and attempt to place mythological narratives on the spectrum from the real to the imaginary. Network theory has recently been developed and applied to polymers, economics, particle physics, computer science, sociology, biology, epidemiology, linguistics and more [1–7,9–11]. A number of statistics (a)E-mail: [email protected] have been developed to capture features of such networks. Some structural properties are quantified using the characteristic path length , the longest geodesic max and the clustering coefficient C. The first of these is a measure of the average minimum separation between pairs of N nodes and max is the diameter of the network. Clustering measures to what extent a given neighbourhood of the network is cliqued. If node i has ki neighbours, then the maximal number of potential edges between them is ki(ki − 1)/2. If ni is the actual number of bonds between the ki neighbours of i, the clustering coefficient of the node is [9] Ci = 2ni ki(ki − 1) . (1) Many complex networks have a modular structure implying that groups of nodes organise in a hierarchical manner into increasingly larger groups. Hierarchical networks are characterised by a power-law dependency of the clustering coefficient on the node degree [12–14],