Hands-on: Who Is Important, and In What Sense
Seven centralities on one network, and the interesting part is where they disagree.
NoteWhere the code lives
This course keeps its lecture note free of runnable code. Everything you execute lives in a marimo notebook, so it stays interactive and reactive instead of being a wall of output frozen into a web page.
Run this notebook — it runs in your browser, with nothing to install and nothing to sign into. The first load takes a few seconds while Python itself is downloaded.
Prefer to work locally? The notebook is in the repository at notebooks/m06-centrality/coding.py. Run it with marimo edit notebooks/m06-centrality/coding.py.
What you will build
The notebook hands you the networks and a worked closeness and Katz cell. The rest is yours to write.
- Compute degree, closeness, harmonic, betweenness, eigenvector, Katz and PageRank on a small social network.
- Implement Katz centrality yourself, including choosing a safe value for the attenuation factor.
- Apply the measures to the Roman road network and map the results geographically.
- Compute the correlation matrix between centralities and interpret it.
What to watch for
- Find the node whose betweenness rank is far above its degree rank. Look at where it sits — that is a broker.
- Set the attenuation factor above 1/\lambda_{\max} in your Katz implementation and watch it break. Understanding the failure is the point.
- Compute the correlations on a star graph and on a path graph. Near-total agreement in one, near-total disagreement in the other.