At their most basic, social networks comprise nodes or vertices that represent individuals or groups, and edges or links that represent some relationship between the nodes. Generally, each set of nodes can have different relationships described by different networks. I am interested only in simple unweighted networks, in which the relationship is two-way and cannot link one node with itself.
Networks have a variety of properties defined and measured by analysts. Some of these properties concern the structure of the network: such as the number of edges running from each node (degree distribution). Others concern processes that occur over the network, such as the speed with which an infection can reach some proportion of nodes, or the capacity for pockets of believers to hold out against a competing belief. I am interested in methods to describe useful properties, and how values of some properties constrain the feasible values of other properties. After all, it is impossible to recognise unusual properties of real-world networks without already being able to identify the usual properties.
Badham, J., Kee F. & Hunter, R.F. (2018), 'Simulating network intervention strategies: Implications for adoption of behaviour', Network Science, vol. 6, no. 2, pp. 265-280.
Badham, J. M. (2013), 'Commentary: Measuring the shape of degree distributions', Network Science, vol. 1, no. 2, pp. 213-225.
Badham, J. M. & Stocker, R. (2010), 'The impact of network clustering and assortativity on epidemic behaviour', Theoretical Population Biology, vol. 77, no. 1, pp. 71-75.