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Mathematics LibreTexts

5.E: Using matrices to represent social relations (Exercises)


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Review Questions

1. A matrix is "3 by 2." How many columns does it have? How many rows?

2. Adjacency matrices are "square" matrices. Why?

3. There is a "1" in cell 3,2 of an adjacency matrix representing a sociogram. What does this tell us?

4. What does it mean to "permute" a matrix, and to "block" it?

Application Questions

1. Think of the readings from the first part of the course. Did any studies present matrices? If they did, what kinds of matrices were they (that is, what is the technical description of the kind of graph or matrix). Pick one article, and show what the data would look like, if represented in matrix form.

2. Think of some small group of which you are a member (maybe a club, or a set of friends, or people living in the same apartment complex, etc.). What kinds of relations among them might tell us something about the social structures in this population? Try preparing a matrix to represent one of the kinds of relations you chose. Can you extend this matrix to also describe a second kind of relation? (e.g. one might start with "who likes whom?" and add "who spends a lot of time with whom?").

3. Using the matrices you created in the previous question, does it make sense to leave the diagonal "blank," or not, in your case? Try permuting your matrix, and blocking it.

4. Can you make an adjacency matrix to represent the "star" network? what about the "line" and "circle." Look at the ones and zeros in these matrices -- sometimes we can recognize the presence of certain kinds of social relations by these "digital" representations. What does a strict hierarchy look like? What does a population that is segregated into two groups look like?