Analysis of kinship relations with Pajek
In this paper we present an approach to analysis of large genealogies using multirelational networks and network multiplication (matrix multiplication of network matrices) implemented in the program Pajek. Fast multiplication algorithm was developed which can be used for very large sparse networks. In general the network multiplication is a ”dangerous” operation since the product network can be denser than the operand networks - resulting in available memory overflow. But in some cases we know from the nature of the product network that it is also sparse. In these cases (and for smaller networks) the network multiplication can be a powerful network analysis tool. This is the case in analysis of genealogies. Genealogies can be represented as networks in several different ways: as Ore graphs, as p-graphs, or as bipartite p-graphs. For some purposes p-graphs are more suitable (e.g. searching for relinking marriages) while for others (e.g. calculating kinship relations) Ore graphs are more convenient. In the last versions of Pajek these types of networks are represented as multi-relational networks - for example the p-graphs with relations is a son of and is a daughter of. Using matrix multiplication we can compute from some basic relations all other kinship relations ( is a grandparent of, is a sibling of, is a brother of, is a wife of , is an aunt of ...). We will demonstrate the approach on some large genealogies.