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Mathematics LibreTexts

2.4: Seeing patterns

  • Page ID
    7656
  • [ "article:topic", "authorname:rhanneman" ]

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    The third, and final reason for using "formal" methods (mathematics and graphs) for representing social network data is that the techniques of graphing and the rules of mathematics themselves suggest things that we might look for in our data — things that might not have occurred to us if we presented our data using descriptions in words. Again, allow me a simple example.

    Suppose we were describing the structure of close friendship in a group of four people: Bob, Carol, Ted, and Alice. This is easy enough to do with words. Suppose that Bob likes Carol and Ted, but not Alice; Carol likes Ted, but neither Bob nor Alice; Ted likes all three of the other members of the group; and Alice likes only Ted (this description should probably strike you as being a description of a very unusual social structure).

    We could also describe this pattern of liking ties with an actor-by-actor matrix where the rows represent choices by each actor. We will put in a "1" if an actor likes another, and a "0" if they don't. Such a matrix would look like figure 2.1.

    Figure 2.1.  Matrix representation of "liking" relation among four actors
      Bob Carol Ted Alice
    Bob

    ---

    1

    1

    0

    Carol

    0

    ---

    1

    0

    Ted

    1

    1

    ---

    1

    Alice

    0

    0

    1

    ---

    There are lots of things that might immediately occur to us when we see our data arrayed in this way, that we might not have thought of from reading the description of the pattern of ties in words. For example, our eye is led to scan across each row; we notice that Ted likes more people than Bob, than Alice and Carol. Is it possible that there is a pattern here? Are men are more likely to report ties of liking than women are (actually, research literature suggests that this is not generally true). Using a "matrix representation" also immediately raises a question: the locations on the main diagonal (e.g. Bob likes Bob, Carol likes Carol) are empty. Is this a reasonable thing? Or, should our description of the pattern of liking in the group include some statements about "self-liking"? There isn't any right answer to this question. My point is just that using a matrix to represent the pattern of ties among actors may let us see some patterns more easily, and may cause us to ask some questions (and maybe even some useful ones) that a verbal description doesn't stimulate.