# The complex social network of surnames: A comparison between Brazil and Portugal

## TL;DR

This study analyzes social networks based on family names in Brazil and Portugal, revealing differences in societal miscegenation and network properties like power-law degree distributions and small-world features.

## Contribution

It compares surname-based social networks in Brazil and Portugal, highlighting differences in miscegenation and network topology, including power-law distributions and small-world characteristics.

## Key findings

- Portuguese society has higher miscegenation than Brazilian society.
- Degree distributions follow an inverse square power law.
- Networks exhibit small-world properties and negative assortative mixing.

## Abstract

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.