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Evil in Social Networks

Evil in Social Networks is the study of the representation of evil in dramas. Rather than focusing on evil itself, it concentrates on how evil is perceived and represented in social networks and dramas. The perception of evil, differs from one point of view to another and is not always absolute. By viewing evil through the lens of dramas, we are able to analyze the representation of evil. Dramas have the power to shift evil into stark contrasting black and white, as opposed to reality, where evil can more often appear in black, white, and grey.

Applying the concept of evil to social networks can be considered dangerous or unethical. It can be unacceptable to define a typical member of the the community, or a node in a social network, as “evil”. Dramas, however, can be used as bridges between the ethics of real life, and social networks and that can be used in order to study evil. Since we grapple with the representation of evil instead of evil itself dramas are a natural testing ground.

The subject is discussed in the Book "Analyzing narratives in social networks: taking Turing to the arts" by Zvi Lotker, A professor at the Faculty of Engineering, Bar Ilan University.

Related Work

Human thought and religion tackle the concepts of good and evil, as well as the tension between the two. Several religions define “evil” as a relative concept, while others perceive evil as absolute. In the context of social networks, bullying is a well-studied example of evil (or at the very least, bad behavior) in social networks. Bullying is considered to be inappropriate behavior, both online and in the real world. Another form of bullying is cyberbullying which is an attack on the Ego network of the victim.

Evil as the Destruction of Social Fabric

The definition of evil that we use coincides with that of Spinoza. Spinoza defines good and evil in the following way.

"By good I shall understand what we certainly know to be useful to us... By evil, however, I shall understand what we certainly know prevents us from being masters of some good"

We define evil as the destruction of the social fabric. Social fabric, which weaves society together, is composed out of many triangles, comprised of three mutual acquaintances within a graph. High clustering coefficient are a universal property of social networks. These clustering coefficients essentially count the number of triangles and then divide the total by the maximum number of triangles possible.

Clustering Coefficient Formula:

$GC(G)={\frac {3(NumberOfTriangles)}{NumberOfConnectedTriplesOfVertices}}$

In graph theory, a clustering coefficient is a measure of the degree to which nodes in a graph tend to cluster together. Evidence suggests that in most real-world networks, and in particular, social networks, nodes tend to create tightly knit groups characterized by a relatively high density of ties. This likelihood tends to be greater than the average probability of a tie randomly established between two nodes.

Clustering Coefficient Formula to Multigraphs:

$GC_{W}(G)={\frac {\textstyle \sum _{i\in {1,...,n)}}a_{i,i}^{3}\displaystyle }{\textstyle \sum _{i\neq j\in {1,...,n)}}a_{i,j}^{2}\displaystyle }}$

where $a_{i,j}^{k}$ is the element i, j of the adjacency matrix A to the power of k.

In the context of evolving social networks, the clustering coefficient becomes a function of time. In the context of a link stream evolving social network, this function usually increases over time. Formally, the global clustering coefficient is $GC_{W}(t)=GC_{W}(G(t))$.

Normalized Weighted Global Clustering Coefficient Formula:

$GC_{W}(t)={\frac {CG_{W}(t)}{max_{\tau }CG_{W}(\tau )}}$

In conclusion, according to Spinoza’s definition of evil, it is clear that social fabric is good. Therefore, the destruction of the social fabric can be defined as evil.

social networks have high clustering coefficients. This means that social networks tend to have many triangles. These triangles form the building blocks of the social structure. Through these triangles, individuals (or nodes) can verify information efficiently. The destruction of the social fabric is therefore the destruction of the triangles, since this causes the social network to resemble a tree instead of its own social fabric, which is composed of many triangles. In general, this destruction amplifies the power of those individuals who are located in central positions in the social network. Moreover, this allows the central players to manipulate the other players, and robs the non-central players of their ability to verify information. Following Spinoza, these scenarios are evil.

One effective way of deleting triangles without destroying the connectivity of the network is increasing the size of simple cycles without chords. In general, a cycle is a path where the beginning of the path is equal to the end of the path. The size of the cycle is the number of different vertices in the path. A directed cycle is a directed path, where the first vertex is the last. The size of the directed cycle is the number of different vertices.

According to the definition, social networks which are missing many triangles have been generated through evil deeds. Therefore, when trying to answer the question of whether or not a drama deals with evil, it could be spotted as an area in the network which is missing many triangles or large cycles without chords.

Representation of Evil in Dramas Viewed Through Space

Finding large cycles in a graph is a well-known NP-hard problem. This problem boils down to finding Hamilton cycles. However, detecting the smallest cycle beginning from a specific node can be solved easily by using a breadth-first search (BFS).

The following simple algorithm can be used to find the smallest large cycle in a social network of a drama. To find the smallest large cycle, from each node v, run a BFS starting with node v, and then find the smallest cycle beginning from node v. Then, look at the largest cycle of the resulting cycles. If this cycle is large, this provides evidence for the destruction of a social network. Where there is destruction of a social network, there is evil. The size of a “large” cycle varies, However, in general, a cycle of size 5 is on the fence, and a cycle of size 6 or larger is typically large.