Weighted Graph: Make SNA More Accurate

In the latest three lectures, we are in touched with Social Network Analysis (SNA), which is a key component of the Social Network Research Field. And we get a superficial understanding of the different algorithm defined in SNA by doing some exercise on and after classes. And a question came to my mind afterwards. Did the social graph correctly represent the relations between human beings in SNS?

Let’s have an exercise to find the problem.

We assume that 5 people (From n1 to n5) are in the same SNS and their relationship can be represented by the graph below (Graph1).

Graph1: Normal Graph

Then we will use some algorithms in SNA to analysis it.

Degree Centrality: Cd(ni) C’d(ni) n1 4 1 n2 1 1/4 n3 3 3/4 n4 2 1/2 n5 2 1/2 Cd = 0.667	Closeness Centrality: Cc(ni) C’c(ni) n1 1/4 1 n2 1/7 4/7 n3 1/5 4/5 n4 1/6 2/3 n5 1/6 2/3 Cc = 0.26
Betweenness Centrality: Cb(ni) C’b(ni) n1 7/2 7/12 n2 0 0 n3 1/2 1/12 n4 0 0 n5 0 0 Cb = 0.5625

From the results of SNA, we can get some information:

1. The SNS shown by Graph1 is with high Degree Centrality and Betweenness Centrality.

2. Node n1 is the most important node in this SNS (with highest Cd, Cc and Cd).

However usually the relationships in the real SNS are not such simple, there are thousands types of relationships, for example, Tim and Bill are best friends while Tom and Sissy were just got to know, and obviously the strength of two previous relationships are not the same so I think it is unfair to assign all relations in SNS with the same value 1.

Let’s use the case showed by Graph1 again and adding some additional information: (1) n3 and n4 are best friends. (3) n3 and n5 are old friends. (4) n1 is a friend of n2 (5) n1 was just got to know n3, n4 and n5.

And this time we divide the relations into 4 levels and use a weighted graph to represent their relations again, as shown in Graph2.

Graph2: Weighted Graph

Now do the SNA again with the same algorithms.

Degree Centrality: Cd(ni) C’d(ni) n1 5/4 5/16 n2 1/2 1/8 n3 2 1/2 n4 5/4 5/16 n5 1 1/4 Cd = 0.333	Closeness Centrality: Cc(ni) C’c(ni) n1 1/14 2/7 n2 1/20 1/5 n3 3/37 12/37 n4 3/40 3/10 n5 3/41 12/41 Cc = 0.256
Betweenness Centrality: Cb(ni) C’b(ni) n1 Unfinished Unfinished n2 Unfinished Unfinished n3 Unfinished Unfinished n4 Unfinished Unfinished n5 Unfinished Unfinished Cb = Unfinished

Due to time limited, I cannot finish the calculation of Betweenness Centrality (Awful complex, I’m afraid (- -#)) and there may be some mistakes in calculation, but the result changes a lot:

1. Degree Centrality of the SNS getting lower, it is about 1/2 of the previous SNA.

2. Node n3 becomes the most important node (with highest Cd and Cc), while in the previous SNA it is n1.

In conclusion, the result completely changed when we take the weight of the relationships into consideration, and I believe using weighted graphs is a more reasonable and humane way to do SNA (If you do not consider the weight of relations to analysis the second case, the result will be unconvincing).

References:

• Angela Bohn & Norbert Walchhofer & Patrick Mair &Kurt Hornik: Social Network Analysis of Weighted Telecommunications Graphs
• M. E. J. Newman: Analysis of weighted networks
• http://toreopsahl.com/tnet/weighted-networks/node-centrality/

Epistemic Aim:Individual vs.Social

PART 1 --- An experiment: Individual vs. Social

We did an experiment in the last class, which is about the different of individual cognition and social cognition.

First we read a part of paper about Social Cloud, and then gave comments and thought about questions individually. Here are my individual answers (this is class activity one):

1. What is the definition of Social Cloud?

A Social Cloud is a resource and service sharing framework utilizing relationships established between members of a social network. – Answer from the paper (Unchanged after searching the Internet)

2. What are the possible applications of a Social Cloud?

Social Computation Cloud, Social Storage Cloud, Social Collaborative Cloud, Social Cloud for Public Science, Enterprise Social Cloud. –Answer from the paper

Friend Networks, Identification, Data Formats – Answer from the Internet

After that, we assembled our ideas and had a discussion on the same questions together by using a Google-doc, and finally we got the answers of the same questions, I also changed my answers and listed them (this is class activity two):

1. What is the definition of Social Cloud?

A Social Cloud is a scalable computing environment in which virtualized resources contributed by users are dynamically provisioned amongst a group of friends or colleagues. – Collect from group members

2. What are the possible applications of a Social Cloud?

Social Computation Cloud, Social Storage Cloud, Social Collaborative Cloud, Social Cloud for Public Science, Enterprise Social Cloud. – Keep unchanged.

PART 2 --- Behind the experiment: A change of epistemic aim

Actually, we only changed a little about the two answers after discussion, but even a little change makes a big difference, and the difference is included in our Group doc, instead of listing our answers and voting for the best one, we gave comments to other member’s answers or gave comments to comments, searched for references and evidences and absorbed ideas from others, even one of the group members listed the definition and applications of Cloud Computing (P.S. This concept a little-bit overlaps the concept of social cloud). It seems that our epistemic aim was changing trough the discussion. Take myself as an example, in activity one, I was concentrated on the paper in order to understand the concept, so in this part, my main epistemic aim was to answer the two questions, so my answers mainly based on the paper, in other word, I used functions of cognition and metacognition at that time and never in touch with the Epistemic Cognition level. But when editing the Google doc (Activity two), I seldom considered the content of the paper but focus on the other’s answers and comments to improve my knowledge of Social Cloud by gong through the references giving by others and writing down my own opinions, this is something about higher levels of cognition. And my epistemic aim totally changed.

PART 3 --- Conclusion

Using social ways to do idea generation and knowledge management is more effective. And it is more likely to ‘Think out of box’ by discussion in a social network environment because our epistemic aim changed a lot.