DATA ANALYSIS: SOCIAL NETWORKS

Only connect

Felix Grant looks at the application of data analysis software to social networks

Once upon a time I spent several weeks, completely alone (long story; don’t ask), on top of a mesa with a precarious microecology, surrounded by desert. My only company was the local wildlife: mostly lizards, small rodents, and an unlikely colony of feral cats at the top of the food chain. Those cats, as the only visible social

species, became the focus of my attention for much of the time – particularly the complex network of behavioural relations that bound their tribe together. There were mentor/mentee relations. There were sibling and parent/offspring relations. There were hunting partners. There were bonded sexual pairings and temporary liaisons. There was a power hierarchy. And there was a rich web of what I could only describe as ‘best friend’ relations. Then there was also a small number

Lexicon

Networks look slightly different from their various fields of application, with nomenclature varying considerably across the literatures. My own background inclines me to nodes, arcs and regions, but SNA usually talks of actors and edges, with regions usually ignored. Here, with feline illustrations, is a quick tour of the most common terms. Actor (node, vertex): basic network

element, drawn as a dot or as a hollow shape. In my feral colony, each cat would be an actor. Sometimes coloured or otherwise coded to represent attributes, for example red for male, blue for female, and/or square for mentor and circular for mentee. Edge (arc): connection, drawn as a line,

between two actors. A partnered hunting pair of cats would be represented as two actors connected by one edge. A weighted edge has a numerical value associated with it – perhaps the food yield productivity of their partnership. A directed edge indicates the sense of a relation – a mentor or parent

of maverick individuals who appeared to be entirely outside all of this, part of the tribe, but operating alone, connected to the main only by apparently random acts of altruism or brigandism. Studying systems of inter-relational linkage

was, at that time, an important part of my day job. But computing resources were scarce in those days, and sheer volume of content and association limited what could realistically be done; things are very different today. While analysis of social networks stretches back at least to the 1940s (arguably to the late 19th century), and social network analysis (SNA) as a formal field has been well established in sociology (to which I shall return, shortly) for decades, ‘it has only recently been discovered by behavioural biologists as a useful tool in the study of animal behaviour’, to quote

relation would be directed, but a sibling relation would not. Multiplicity is more than one edge connecting the same pair of actors, such as a sexually bonded pair, which also hunts together. A navigable consecutive sequence of actors and edges, beginning and ending with actors, is a walk. For example, if Cat A is the mentor of Cat B, and Cat B is the mother of Cat C, there is a walk from A to C comprising two edges (the length of the walk is said to be two) and three actors. In this example, the walk is also a trail, since no edge is traversed more than once. The shortest walk connecting two specified nodes is a geodesic. Order is the number of actors in a network

or clique, while size is the number of edges. A clique is a group of actors in which every actor has a connection to every other. Every kitten in a litter, for example, is an actor with an identical (sibling relation) edge linking it to every other kitten in that same litter. The order of a clique is the number of actors connected by it, a k-clique being a clique of order k.

A network map for a small subset of the feral mesa cat tribe is begun in Simile

Amelia Coleing in Bioscience Horizons just over a year ago. Coleing goes on to observe that ‘...methods devised to measure social complexity in studies of animal behaviour... often reflect the social relationships between individuals indirectly... social network analysis provides formal descriptors... and by providing quantitative measures... allows testing of statistical models about relationships and structure’. Coleing emphasises the use of SNA as a

tool particularly suitable for studying small, captive populations of obligate social species in restricted territory, her own work focussing on 10 elephants in a zoo. Each of those specifications makes for better control of data capture and, therefore, better data quality. Interconnection complexity increases rapidly with population size, populations that are wild or spatially unconfined may be impossible to observe continuously in toto, and social relations that are not obligate introduce numerous uncertainties. This doesn’t, however, mean that SNA

methods are not more widely applicable; their widest application, in fact, has been to less controlled circumstances. One study by Julian Drew, for example, seeks to learn lessons about tuberculosis transmission through examination by SNA techniques of the relation between infection and social interaction among wild

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SCIENTIFIC COMPUTING WORLD JUNE/JULY 2010

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