# Comparing Centrality Measures.

Using small scale graphs ( or networks ) at first, student will compute degree centrality, closeness/farness centrality, and betweenness centrality for the purpose of comparing these measures and developing an intuition for what these measure can tell us about individuals in a social network.

## Overview

Students will explore metrics of node
centrality (degree, closeness, and betweenness) and develop an intuition for
what these actually measure in the context of a social network. At first, students
will compute these metrics by hand for specific graphs with a small number of
nodes and edges. These preliminary
computations are designed to help the students warm up to the quantitative side
of network analysis and help demystify the math from the definition of the
metric. We will look at some standard
mathematical graphs (complete graph,
tree, “simple chain”, simple cycle) and then extend into small-scale
graphs with less structure. We will
select these more generic graphs to specifically highlight the differences
between degree centrality, closeness centrality, and betweenness
centrality.
As the assignment progresses, we apply some of
the observations from our warm-up to think about these metrics in the context
of a social network. The nodes now
become people, and edges represent “interactions” between these people. Students attempt to interpret these
centrality metrics in this new context.

For example,

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For example,

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For example,

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*In what ways is a person with a high degree centrality different from a person with a high closeness centrality? Does one imply the other?*In the last component of the assignment, students begin working with large scale graphs and using NodeXL. Given a provided social network, one familiar to the students, have them hypothesize how centrality measures for pairs or groups of characters will compare.For example,

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*Will Prof. McGonnagall have a higher closeness centrality than Dumbledore? Describe your reasoning.*Then, using NodeXL, they can explore whether their intuition was correct. The assignment will end with students putting together a summary of the different metrics, how they are defined, and what information they can provide about people in a social network. We will ask students to use specific examples from social networks to support their explanations.