Sociomatrix --Reflect of Lecture 7 & 8 & 9

Recently, I have learnt many interesting concepts about the social network analysis including not only meaningful but also useful calculation from the lectures. All the content in class inspired me a lot and I want to pick the sociomatrix, one important property of the social network analysis, to share with you.

Before giving the description and explanation of sociomatrix, let’s introduce the sociogram first.

Sociogram is a graphical representation of social networks. It can help us see the interactions in the social networks intuitively. Prof. Chan showed us the sociogram of our blogosphere. You can easily find the interesting interaction of your own in the previous period of writing blog and giving comments to others’ blogs.

Figure 1 Sociogram of blogosphere

You may see that some are isolated yet some are tightly connected with others, those relationships are showed as lines between the individuals. The sociogram is performed well in human eyesight to see the relation. But how can we let the computer know or aware of that information as well? In other words, before the computer doing the social network analysis, it must have some basic data, like the connection between whom and whom, to calculate.

We might aware that any one of those connections involves only two individuals. And even considering the directed graph, it still involves two nodes. That property might already inspire you to think the relationship as a way of mathematics, like matrix.

Matrix of two dimensions is exactly prefect for indicating the relationship between two things. If we put the elements the same sequence both at the horizontal and vertical direction, or you can say the row and the column, and we use 1 and 0 to represent that there is a connection between the two elements or not, we have a matrix as we expect. The matrix is for the social network and we can give it an exclusive name, sociomatrix.

We give the definition of the sociomatrix if we consider the directed sociogram as follows:

For the pair<ni,nj>, which means the element ni of the social network point to the element nj in the socogram, we regard Xij as the value (1 for yes and 0 for no) that is there a tie from the ni to nj on the relation. The diagonal elements are usually undefined because SNA ignore the “self-choice” element.

We take another simple sociogram as example to intro the sociomatrix and we know that B points to C but not vice versa. We can get the idea that X23 equals to 1 and X32 equals to 0, just exactly represent the relationship in the sociogram. Then we have a clear idea about Xij: From the view of row, element i choose element j. From the view of column, element i is chosen by element j.

Figure 2 Sociogram of 4 people's relation

	A	B	C	D
A	-	0	1	1
B	0	-	1	1
C	1	0	-	0
D	1	1	0	-

Chart 1 Sociogram transform to Sociomatrix

Figure 3 Sociomatrix of  4 people's relation

Sociomatrix can not only represent the link of elements but calculate to find the potential relationship with the operation like transpose, addition, subtraction, multiplication and even power.

Power of the sociomatrix may be the most difficult to understand. But after discussion and reflection, we can clearly know the product of a sociomatrix can show the walk of length. With the help of the matrix, the social network analysis seems to be much more reliable and interesting.

Figure 4 Discussion on the power of sociomatrix in class

What’s more, there are many other concepts like actor centrality and actor prestige which contain fascinating calculation and information. Wish to learn more knowledge in the next lecture!