  We present a study of social networks based on the analysis of Brazilian and
Portuguese family names (surnames). We construct networks whose nodes are names
of families and whose edges represent parental relations between two families.
From these networks we extract the connectivity distribution, clustering
coefficient, shortest path and centrality. We find that the connectivity
distribution follows an approximate power law. We associate the number of hubs,
centrality and entropy to the degree of miscegenation in the societies in both
countries. Our results show that Portuguese society has a higher miscegenation
degree than Brazilian society. All networks analyzed lead to approximate
inverse square power laws in the degree distribution. We conclude that the
thermodynamic limit is reached for small networks (3 or 4 thousand nodes). The
assortative mixing of all networks is negative, showing that the more connected
vertices are connected to vertices with lower connectivity. Finally, the
network of surnames presents some small world characteristics.
