Chapter 4 Network Data and Measurement

4.1 Types of network data

4.1.1 One mode data

One-mode data is network data with one vertex class and can be represented as an adjacency matrix. Simple examples include organizations, individuals, concepts etc.

4.1.2 Two mode data

Let A be an \(N \times M\) incidence matrix; the row-projection of A is the \(N\times N\) matrix B such that \(B_{ij}=\sum_{k=1}^M A_{ik}A_{jk}\); likewise, the column projection of A is the \(M\times M\) matrix C such that \(C_{ij}=\sum_{k=1}^N A_{ki}A_{kj}\)

Matrix notation \(B=AA^T\) and \(C=A^TA\).

To analyze network data, we must first collect it. Many approaches exist Ð some better than others for particular purposes, this is a complex topic overall, but we will at least skim the surface

Two important concepts (not always separable):

Common way to elicit ego nets: complete instrument followed by roster

We have briefly mentioned this form of data collecting before. One is asked to name those with whom you discussed important matters Then, asked to fill in same question for all pairs of persons named initially (see ). Pros: Relatively easy to administer; don’t need entire list of possible alters; don’t have to ask about all group members. Cons: Step 1, step 2 questions have different error rates; may need large roster if many alters; hard to use with paper-based surveys

Can also think of coding schemes for archival materials as ``instruments"

How do we define the node or vertex set? If misspecified, theoretically relevant ties may be missed.

Major distinction: local versus global properties. Different sampling methods needed for each.