Network analysis glossary
Communities and modularity
A community is a group of people who are more tied to each other than to the rest of the network. Community detection finds those groups from the ties alone. Modularity is the score it maximises: how many more ties fall inside the groups than chance would predict.
Updated · Netgraf
| Group | Members |
|---|---|
| Group 1 (12) | Mr. Hi, Member 2, Member 3, Member 4, Member 8, Member 10, … |
| Group 2 (11) | Member 9, Member 15, Member 16, Member 19, Member 21, Member 23, … |
| Group 3 (6) | Member 24, Member 25, Member 26, Member 28, Member 29, Member 32 |
| Group 4 (5) | Member 5, Member 6, Member 7, Member 11, Member 17 |
4 communities found with the Louvain method, modularity 0.419. Computed live from the example map with the same code the Netgraf insights panel runs.
Modularity
Q = (1 / 2m) * sum over pairs i, j of [ A(i,j) - k(i) k(j) / 2m ] * same(i, j)
Mark Newman's modularity compares each group's internal ties with the number you would expect if the same people kept their degrees but were wired at random. Trying every possible split is impossible for all but tiny networks, so algorithms search for a good one. The Louvain method (Blondel and colleagues, 2008), which Netgraf uses, merges people and then groups greedily while modularity keeps rising.
Zachary's karate club
Wayne Zachary recorded the friendships among 34 members of a university karate club just before a dispute between the instructor (Mr. Hi) and a club officer (John A.) split it in two. The split followed the friendship network so closely that community detection run on the pre-split ties recovers almost exactly who left with whom. It is the standard test for every new algorithm. Louvain typically finds four groups rather than two: the two factions, each with a tighter core.
In Netgraf
The Insights panel lists Groups: "people who are more tied to each other than to anyone else", each named after its best-connected member. Choose Colour the map by group and every dot takes its community's colour while the lines go neutral.