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Arianto, Tomi
Universitas Negeri Medan
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Struktur Graf Berarah pada Sistem Kekerabatan Batak Toba (Dalihan Na Tolu) Mey Gracia Sitanggang; Rawiyah; Goffri Simarsoit; Ian Pedrosa manatap Lumban Gaol; Hery Judika Lumban Tobing; Tomi Arianto
JUMAT: Jurnal Matematika Vol. 3 No. 2 (2025): JUMAT, Desember 2025
Publisher : Institut Agama Islam Negeri Fattahul Muluk Papua

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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.
Co-Authors Adira Cahya Adrias Affandi, Yaszmin Putri Afriana Afriana Afriana Afriana Afriana Afriana, Afriana Agus Sutardjo Ahmad Samhudi Ambalegin Ambalegin Ambalegin, Ambalegin Anastasia Juwita Ningsih Angel Purwanti Angelina, Veren Anggreini, Heny Aprilia, Isnanda Arfiani, Nanda Tiara Ayu Anggraeini Br. Simbolon Ayu Nadira Nadira Wulandari Ayu Nadira Wulandari Azhari, Chud Radeffy Aziz, Basyarul Carmel Auta Sitepu Chairunnisa, Hera Cheristine Aprilia Cinta, Cinta Damanik, Bea Anantha Desica Desica Desria Natalia Sirait Elfi Rahmi Fadhilah Sabrina Zaylani Fahmy Dalimunthe, Syairal Farasi, Tessa Anastasia Febri Yulika Febriani, Jeany Jean Ghafari, M. Oky Fardian Ginting, Dea Veronika Br Ginting, Natalia Goffri Simarsoit Grace Libra Sinurat Griselda Giovanni Simanjuntak Gulo, Merlin Soviana Hadawiyah, Andina Hanus Tewarat, Sipri Harianja, Berlian Serevina Harry Yoesoef Pabiona Hasibuan, Hotna Ria HENDRA KURNIA PULUNGAN, HENDRA KURNIA HERA CHAIRUNISA, HERA Hery Judika Lumban Tobing Hotman Nasution Hotni Purba Tondang Ian Pedrosa Manatap Lumban Gaol Icha Sartika Indri Yani, Indri Intan Valiza Jamba , Padrisan Jamba, Jamba Jeany Jean Febriani Jesica, Verenanda Juliana Adelina Purba Karmila Alam Syah Wellem Khairun Nisa Khairunnisa Khairunnisa Kholijah, Nita Laila Adisti Aulia Lavinia Rosemary Ledy Novwanty Nainggolan Lismalinda M. Oky Fardian Gafari Maharani, Puja Manuela Indriati Siahaan MARA UNTUNG RITONGA, MARA UNTUNG Marson Goh Maulid Hariri Gani Mendrofa, Novi Oktavia Mesya Fadila Sani Harahap Mey Gracia Sitanggang Michelle Intan Goh Rumengan Waworuntu Mika Charolin Mirda Aryadi Muhammad Fikri Munthe, Samantha Mariani Mutia Rafael Nabila Aswari Lubis Nainggolan, Santa Elfira Najwa Fitri Sahira Nazwa Annisa Nitasri Murawaty Girsang Nolen Nolen Nopriadi Nopriadi Noviana Osinta Bere Novita, Elmi Nurma Dhona Handayani Nursalassaty Padrisan Jamba Pegi Fortunela Pijar Omar Piscesco Putri Dhea Sapitri Putri Silvia Putri, Saibil Aprilia Rachel Esteria Siagian Rahardy, Iffah Fauziah Rawiyah Resneri Daulay Reviani Manullang, Ester Reynaldi Hutapea Ricky Ricky Ridho Sastro Panjaitan Rinaldi Panjaitan, Rinaldi Rini Syarifah Rizki, Sestri Novia Rusmitha Sipahutar Ruth Sofia Rolenza Lumbanraja Saibil Aprilia Putri Sanada Manalu Selvina Silalahi Septiani Sihaloho, Jelita Septriani Septriani Septriani Septriani Septriani Septriani Septriani Septriani Septriani, Septriani Shite, Yohan Tio Pantaria Siallagan, Lasenna Sihombing, Noel Sihombing, Rosi Anita Simangunsong, Cladeo SIMANJUNTAK, DAIRI SAPTA RINDU Sitanggang, Romauli situmorang, Dina Evianna Suryani, Melly Siska Susan Tamara Hasibuan Syafitri, Astrid Syahfitri, Rindani Syairal Fahmy Dalimunthe Syielvi Dwi Febrianty Tampubolon, Nico Jacksen Tarigan, Ansi Br Ulfa, Syafrina Vita Nancy Manurung Wina Etami Yusnika Sihite Zahra, Naila Zai Alpris Wulandari Saragih Zakiah, Husnuz Zefri Azharman Zega, Fatizatulo Zia Hisni Mubarak Zuhdi Arman Zuhdi Arman