Structural Balance in Love Triangles
A Love Triangle, also known as an Eternal Triangle, describes a type of romantic relationship that commonly involves three people. Basically, two people compete for the affection of the third person. This scenario is frequently introduced in media and entertainment products. For example, fans of Twilight certainly remember the Love Triangle that involves the three main characters: Bella, Edward, and Jacob. What’s interesting is that Love Triangle perfectly reflects a core concept of networks: Structural Balance.
Based on the definition of the Love Triangle, we could sketch the graph: the nodes are connected by edges with labels “+” representing “romantic relationship” or “-” representing “competitors” (Figure 1). Since Person 2 has a romantic relationship with Person 1, we label the edge +; since Person 3 has a romantic relationship with Person 1, we label the edge +; since Person 2 and Person 3 compete for Person 1’s love as a rivalry, we label the edge -. The Structural Balance Property tells us that the graph is balanced if all three edges are labeled + or exactly one of them is labeled + (the remaining two are -). Therefore, we could conclude that the classic Love Triangle network is structurally unbalanced. Love Triangle’s “instability” is also reflected in the real-life setting: it usually triggers many external and internal conflicts and social stress within this triangular network.
Although there could be many different ultimate results of the Love Triangle, one of the most common ends is that Person 1 chooses Person 2 or Person 3. As a result, the remaining person either ends up hating both of them (Figure 2) or decide to sacrifice for his/her beloved and become friends with them (Figure 3). This change in relationships is supported by the course content, in which there would be implicit forces pushing Person 1 to side with one of Person 2 or Person 3 against the other. The resulting networks are thus structurally balanced according to Structural Balance Property.
We could take The Twilight Saga as an example to better understand “Structural Balance” in a Love Triangle. Competing for Bella’s affection, Edward and Jacob hated each other for most of the stories. This network was, undoubtedly, structurally unbalanced, and we could notice a lot of conflicts among these three main characters. After Bella chose Edward, Jacob decided to be friends with them, resulting in an all + edges among the three nodes network. The conflicts also seemed to get resolved since the resulting network is structurally balanced.
Article: https://screencraft.org/blog/everything-you-need-to-know-about-love-triangles-in-movies-tv/