Networks blog post #1
https://www.pnas.org/content/108/52/20953
The above article talked about the structural balance theory on a global level with very large online social networks. The authors were trying to prove that currently available networks in this world are structurally balanced. Various computational methods were used to determine the overall relationship among all possible networks we have. Structural balance theory was first introduced by Heider, a theory to describe the structure of a network nature in terms of friendship and hostility (positive and negative edges between two nodes). Structures can be balanced in two ways: 1) tensions are completely absent (all nodes have positive relationships with each other. 2) tensions exist between one node and two other nodes while the two other nodes have a positive relationship with each other. The article goes on talking about various analytical methods and how algorithms can be used to prove the structural balance theory. In conclusion, the theory affirms that human societies tend to avoid tensions and conflicts.
I chose this article because it directly relates to what we have learned in class about structure balance theory. In class, we talked about stable triangles vs. unstable triangles. 3 nodes can form a triangle relationship with an edge connecting every pair. There are two situations where the 3 nodes can form a structural balanced network: either 3 positive edges or 1 positive edge exists. This resonates with what the article is talking about above. According to the textbook, a complete graph satisfies the structural balance theory if the three edges between every set of three nodes have 3 or 1 positive edges. This describes a local triangle relationship, what happens if we go from local to global networks? Does this theory still apply? In lecture, the professor discussed two possible situations for a global network to be stable: 1) all nodes have positive edges with each other (all nodes are friends). 2) there exist two groups of friends who dislike each other (each group has all positive edges with local bridges in between that are negative edges). This global network balance leads to a conclusion: balance theorem. The balance theorem states that if a labeled complete graph is balanced, then either all pairs of nodes are friends, or else the nodes can be divided into 2 groups: X & Y, such that every pair of nodes in X like each other, every pair of nodes in Y like each other, and everyone in X is the enemy of Y. This theorem which we learned in class resonates with the main point of the article.