13 Research methods, statistics, critical review and evidence-based practice13.13 Network analysis
13.13.6 Communities, subgraphs and motifs
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Written by Resident Doctor Committee · Published
New in the 2027 syllabus
The College added this topic for exams from January 2027.
Communities and clusters
A community is a group of nodes with relatively dense connections inside the group and fewer connections to the rest of the network.
A cluster, in this setting, usually means the same kind of group. A community does not have to be completely cut off from other groups.
Community detection groups nodes by their pattern of connections. It does not just draw a boundary round points that sit close together in the picture.
Term | What it describes |
|---|---|
Community | A relatively densely connected group |
Connected component | A maximal set of nodes joined by paths, with no path to any node outside it |
Clique | A group in which every pair of different nodes is directly connected |
Two densely connected groups joined by a single edge can be separate communities within one connected component. Neither group needs to be a clique.
Subgraphs
A subgraph contains some of a graph's nodes and edges. Any edge you keep must have both its end nodes included.
An induced subgraph takes a chosen set of nodes and keeps every original edge between them.
A subgraph is not automatically a community. Picking out all the sleep-related symptoms gives a subset, but does not show that they form a densely connected group.
Take a graph with the edges A-B, A-C, B-C and C-D. The subgraph induced by A, B and C is a triangle. Leave out A-C and you still have a subgraph, but it is not induced.
Network motifs
A network motif is a small pattern of connections that occurs more often than expected when compared with a specified set of random networks, and the excess is statistically significant.
Seeing a pattern often is not enough to call it a motif. A pattern can be common simply because the network already has many edges or highly connected nodes.
The comparison networks should keep relevant features of the real network, such as its size and degree pattern (how many connections each node has), while randomising the connections being tested.
Small pattern | Structure | What must be checked |
|---|---|---|
Triangle | Three nodes all connected to one another | Whether triangles occur unusually often compared with the comparison networks |
Feed-forward loop | A points to B, B points to C, and A also points to C | Whether these directed groups of three occur unusually often |
The arrows in a feed-forward loop show the directions recorded in the network. Their shape alone does not prove a causal mechanism.
Interpreting community structure
Modularity compares the connections within proposed communities with the number expected under a specified comparison model.
Community boundaries can shift with the method and resolution setting, so one way of dividing the network is not necessarily the only reasonable one.
Symptom communities may point to groups of related experiences. On their own, they do not establish separate diagnoses or shared biological causes.
Node colours may show categories the researcher chose in advance. The legend must separate these from communities detected from the data.