Within reason, dropping academic vocabulary bombs can be a downright satisfying experience. Thanks to a fascinating paper from the December edition of the Royal Statistical Society, I am pleased to provide you with a tidy little nugget to detonate: Network Theory.

Padraig Mac Carron, a PhD student from Coventry University in London, and professor/colleague Ralph Kenna, had the intriguing idea to use statistical analysis to quantitatively study the characteristics of the social networks built into the Icelandic Sagas. They surmised that realistic social structure would be a strong indication that the sagas were at least loosely based on real people or real groups of people. While there isn't any reliable way to validate their work, the results of their investigation point to the sagas being realistic if not partially factual.

A few definitions are helpful to understand what they did:

__Nodes__: connection points, or in the case of social networks, people

__Links__: connections between points, or relationships

__Degree__: the number of relationships a node has

__Degree distribution__: the probability distribution that describes how many degrees a node is likely to have

__Mean path length__: the mean distance to connect any two nodes in a network

__Clustering coefficient__: the fraction of friend-of-a-friend relationships that are realized for a node

__Small world__: used to describe a network that has a short mean path length and a large clustering coefficient.

__Assortative__: nodes or people with similar numbers of friends are also connected to each other. Interestingly, assortativity is quantified by the correlation coefficient, r, that falls between -1 and +1. Usually we see r as a way to describe how tightly correlated points are on, say, the XY plane.

__Disassortative__: some nodes have many more links than other nodes

__Modularity__: if you didn't know anything about the network *a priori*, how many internal communities would it seem to contain? If the network is only one network, the modularity would be 0. If the community could be split up into many smaller, distantly linked communities, the modularity would approach 1.

What, then, did the authors *do* with all of these ideas... and Vikings? They did what any level-headed statistician would do: compare the sagas to each other and to something known. In this case, they used modern society as the frame of reference. Relative to each other, the sagas had distinct features that reflected the genre of the tales. When clumped together into meta-networks (not a word the authors employed), the 5 largest sagas showed strong overlap. The stories were conceivably written in reference to each other. When all 18 sagas were grouped into one giant network, the authors found that the meta-network was structurally similar to modern society. The mean path length was an achievable 5.5, and the network was small world and assortative. Even more, the huge community had modularity of 0.7 and 9 communities, meaning that the overlap in the sagas would make it impossible to split them back into 18 discrete bunches.

But Nancy, *what does it mean*?

It means that you and I both now have a general understanding of Network Theory. And, it means that Viking sagas are more realistic than you ever knew. I found a cool packages in R to make network plots, so that will be my next post!