Struktur Graf Berarah pada Sistem Kekerabatan Batak Toba (Dalihan Na Tolu)

Abstract

This study aims to examine the structure of the Batak Toba kinship system (Dalihan Na Tolu) using a directed graph theory approach. The Dalihan Na Tolu system is a social philosophy of the Batak Toba community consisting of three main elements, namely hula-hula, boru, and dongan sabutuha, which are interconnected within customary and marital structures. This research employed a qualitative descriptive method with a mathematical modeling approach. Data were collected through interviews, observations, and the study of tarombo documents of Raja Nai Pospos’ descendants, particularly the lineage of Toga Marbun and Lumban Gaol. The data were then represented in the form of tree graphs and directed graphs. The results showed that the Batak Toba kinship system is patrilineal, allowing it to be modeled as a tree graph without cycles in the lineage structure. Meanwhile, customary and marital relations among clans form asymmetric directed graphs because the relationships between vertices have different directions and social meanings. In addition, cycles among clans were identified, representing the concept of mambolahi in Batak Toba customs. The analysis of adjacency matrices, in-degree, and out-degree indicated that several clans have higher levels of social connectivity than others. Therefore, directed graph theory is capable of representing the social structure of Dalihan Na Tolu systematically, visually, and mathematically, while also contributing to the development of social mathematics and ethnomathematics studies based on local culture.