Attack and defense networks in a student social system.

Signed networks are a tool that researchers use to study the relationships between individuals in a complex system. Many studies focus on negative relationships and how these shape the structure of complex networks. Negative hubs, or nodes with the most negative connections, are of particular interest to researchers, as they help us understand social phenomena such as bullying, cyberbullying, and mental health. In this work, we study directed signed networks that represent positive (friendship) and negative (enmity) relationships between students of different academic levels. We propose a systematic methodology to obtain and analyze the networks of nine schools (∼4,300 students) in Yucatán, México. We introduce attack and defense subnetworks constructed from nodes with high out-negative and in-negative degree, respectively, and examine whether these subnetworks exhibit similar structural properties. Using the Leiden algorithm, we detected directed signed communities and compared the community structure of the attack and defense networks. We also calculated social balance theory measures and discussed the outcomes we obtained. We identify a range within which the definition of attack and defense networks is structurally meaningful. We have observed that the structural properties of attack and defense networks are similar and that they are not mutually exclusive, with an average of 60% common nodes, indicating a strong overlap between the two networks. Also, we have evaluated the attack and defense networks in relation to the gender of students, and found that female networks were generally denser across schools. Finally, we discuss the conceptual relationship between these networks and bullying-related roles.