1. Selected Topics in Data Networking
Explore Social Networks: Sentiments and Friendship

2. Introduction Finding cohesive subgroups within a social network
People who belong together tend to interact more frequently than people who do not.
Relations are either positive or negative
Friendship versus hostility, liking versus disliking.

3. Introduction
Expecting positive ties to occur within subgroups and negative ties between subgroups.
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4. Sentiment Analysis
Sentiment Analysis: Detecting and understanding how the audience is reacting to a brand, either positively or negatively.
“I love this company“, “this company” is the topic, and the sentiment (as expressed by the verb “love“) is positive.
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5. Balance Theory
Social psychology is interested in group processes and their impact on individual behavior and perceptions.
In the 1940s, Fritz Heider formulated a principle that has become the core of balance theory
Balance Theory is a motivational theory of attitude change.

6. Structural Balance
Balance Theory is also useful in examining how celebrity endorsement affects consumers' attitudes toward products.
If a person likes a celebrity and perceives that said celebrity likes a product, said person will tend to like the product more, in order to achieve psychological balance.
If the person already had a dislike for the product being endorsed by the celebrity, they may begin disliking the celebrity, again to achieve psychological balance.
Source:

7. Balance Theory
Person feels uncomfortable when he or she disagrees with his or her friend on a topic:
People feel stressed in a situation of imbalance.
P is a person, O is another person (the Other), and X represents a topic or object. P likes O, which is indicated by a positive line between P and O, but they disagree on topic X because P is in favor of it (positive line), whereas O is opposed to it (negative line).

8. Balance Theory Signed graph:
The relationship between two connected nodes can be positive or negative.
Signed graph:
Positive or negative sign is attached to each line indicating whether the associated tie (e.g., an affection) is positive or negative.
Source:

9. Balance Theory
All balanced cycles contain an even number of negative lines or no negative lines at all.
There is one negative line in the cycle, which is an uneven number, so this triple is not balanced.
P, and possibly O, will feel stressed in this situation.

10. Balance Theory

11. Balance Theory Affective relations do not need to be symmetrical.
My feelings for you may differ from your feelings toward me.
Affections are projected from a person to something or someone else.
It is usually better to represent affect ties by arcs rather than edges.
It is easy to generalize balance theory to signed directed graphs:
Ignore the direction of arcs and count the number of negative arcs in each semicycle (a closed semipath).

12. Balance Theory
The sequence of arcs from P to X, on to O, and back to P constitute
Semipath and a semicycle but not a path and a cycle, because not all arcs point toward the next vertex within this sequence.
The semicycle is unbalanced because it contains an uneven number of negative arcs.

13. Balance Theory O’s tie to X is measured from the perspective of P:
It is P’s idea about what O thinks of X, which does not necessarily correspond to O’s real opinion.
In social psychology, this phenomenon is called attribution.
O may have positive or negative affect for P, and if X is a human being (or an animal) rather than a topic, X may also express affections for P and O.

14. Structural Balance
Network analysts are interested in the feelings of all members of a group toward each other.
This has led to the notion of structural balance, which expects balance in the overall pattern of affect ties within a human group rather than in one person’s affections and attributions.

15. Structural Balance
Balanced signed graph can be partitioned into two clusters
All positive edges connect vertices within the same group
All negative edges connect vertices of the two different groups.
Balanced network is extremely polarized because it consists of two factions and actors only have
Positive ties with members of their own faction,
Negative ties with members of the other faction.

16. Structural Balance
Signed graph is balanced if all of its semicycles are balanced.
Find one unbalanced semicycle, the network is unbalanced.

17. Structural Balance
Source: J. Kunegis, Applications of Structural Balance in Signed Social Networks

18. Applications of Structural Balance
International Relations
International politics represents a setting in which it is natural to assume that a collection of nodes all have opinions (positive or negative) about one another
The nodes are nations,
+ and − labels indicate alliances or animosity
Trust, Distrust, and On-Line Ratings

19. Assignment Reading Related Article Answering Questions
See: Computing global structural balance in large-scale signed social networks (PNAS, December 27, 2011, vol. 108, no. 52,20953–20958)
Answering Questions
See the attached file

20. References
Wouter de Nooy, Andrej Mrvar, and Vladimir Batagelj, Exploratory Social Network Analysis with Pajek, Cambridge