Louvain helped us explore the fraud network. But for formal community assignment, we need algorithms that are deterministic, explainable, and give us precise control.
Two algorithms
This lesson covers two foundational algorithms:
Degree Centrality — Counts connections
Weakly Connected Components (WCC) — Finds connected groups
We’ll practice on the Movies graph first, then apply what we learn to fraud detection.
What You’ll Learn
By the end of this lesson, you’ll be able to:
Calculate degree centrality with different orientations and weights
Explain the Union-Find algorithm underlying WCC
Configure WCC with thresholds, seeding, and performance optimizations
Choose between Louvain and WCC based on your requirements
Part 1: Degree Centrality
Degree centrality counts how many relationships a node has.
By default, it counts outgoing relationships. A node with 5 outgoing connections has degree 5.
This is the simplest centrality measure—no iteration, no convergence, just counting. But simple doesn’t mean useless.
Project Movies and Actors
Let’s practice degree centrality on the Movies dataset:
cypher
Project actors and movies
MATCH (source:Actor)-[r:ACTED_IN]->(target:Movie)
RETURN gds.graph.project(
'actors-movies',
source,
target
)
This creates a bipartite graph: Actor nodes connected to Movie nodes. We’ll use this to explore degree centrality before applying it to fraud.
Run Degree Centrality
Count how many movies each actor has appeared in:
cypher
Count movies per actor (outgoing relationships)
CALL gds.degree.stream('actors-movies', {}) // (1)
YIELD nodeId, score
WITH gds.util.asNode(nodeId) AS node, score // (2)
WHERE node:Actor
RETURN node.name AS actor, score AS movieCount
ORDER BY movieCount DESC
LIMIT 15
Streams degree results without writing to the database — useful for exploration before committing
gds.util.asNode() converts internal GDS node IDs back to actual graph nodes so we can access properties like name
Examine results
This query should return a table that looks something like this:
actor
movieCount
Gérard Depardieu
125
Eric Roberts
120
John Wayne
116
Christopher Lee
115
John Carradine
112
Samuel L. Jackson
103
Michael Caine
101
Nicolas Cage
100
Bruce Willis
99
Robert De Niro
97
…
…
This shows the most prolific actors. The degree score equals the number of movies they’ve appeared in.
Orientation Options
You can control in which direction the algorithm should run using orientation:
Orientation
Counts
Use Case
NATURAL (default)
Outgoing relationships
How many movies has this actor been in?
REVERSE
Incoming relationships
How many actors are in this movie?
UNDIRECTED
Forward and back
Both of the above at once
Counting Incoming Relationships
Use REVERSE to count incoming relationships—how many actors are in each movie:
cypher
Count actors per movie (incoming relationships)
CALL gds.degree.stream('actors-movies', {
orientation: 'REVERSE' // (1)
})
YIELD nodeId, score
WITH gds.util.asNode(nodeId) AS node, score
WHERE node:Movie // (2)
RETURN node.title AS movie, score AS castSize
ORDER BY castSize DESC
LIMIT 15
REVERSE counts incoming relationships instead of outgoing — for the Actor→Movie projection, this counts how many actors point to each movie
Filters to Movie nodes only since Actor nodes will have a reverse degree of 0
Note here that the movies in the underlying dataset have a max cast number of 10.
Write Degree to Nodes
Write degree values back to the database for later use:
MATCH (a:Actor)
WHERE a.componentId IS NOT NULL
WITH a.componentId AS componentId, collect(a.name) AS members // (1)
RETURN componentId, size(members) AS size, members[0..5] AS sampleMembers // (2)
ORDER BY size DESC
LIMIT 10
Groups actors by their WCC-assigned component and collects names into a list
Shows only the first 5 members of each component to keep output manageable — large components may have thousands of actors
Examining WCC results
You should get a table that looks something like this:
╒[cols="1,1,3"]
componentId
size
sampleMembers
0
33744
Tasma Walton, Tia Texada, Mikko Nousiainen, Bo Svenson, Victor Adamson
28480
32
Bernadette McDonald, Jimmy Chin, Lakpa Dendi, Barry Blanchard, Gesman Tamang
28400
19
Jo Herbst, Barbara Hintz, Karl Krüger, Ingetraud Hinze, Ernst Pittschau
34381
18
Charlie Kirk, Alice Dewey, Lisa Fox, Larry Elder, Sebastian Gorka
…
…
…
You’ll likely see one giant component containing most actors (the "main" Hollywood network), plus several smaller isolated groups. This is typical of collaboration networks.
Examine Component Distribution
See how components are distributed by running the algorithm in stats mode:
cypher
Component size distribution
CALL gds.wcc.stats('actor-network', {})
Return just one stats fields
If you don’t care about all the stats, and you just want to see the communityDistribution field, you can use YIELD and RETURN to specify:
Louvain might assign a user to community A in one run and community B in the next. WCC always produces identical results.
Determinism matters
This matters when:
Fraud investigations face legal scrutiny
You need to explain why someone was flagged
Results must be reproducible for audits
Downstream systems depend on stable IDs
WCC Finds Components Based on What You Project
This is WCC’s power: you define what "connected" means.
Project all relationships → WCC finds everyone who’s reachable
Project only specific relationships → WCC finds targeted groups
Part 3: Advanced WCC Configuration
Weighted WCC with Thresholds
Not all connections are meaningful. A single shared movie differs from ten shared movies.
Use threshold to ignore weak connections:
cypher
WCC with threshold
CALL gds.wcc.stream('actor-network', {
relationshipWeightProperty: 'collaborations', // (1)
threshold: 5.0 // (2)
})
YIELD nodeId, componentId
WITH componentId, collect(gds.util.asNode(nodeId).name) AS members
WHERE size(members) > 1
RETURN componentId, size(members) AS size, members[0..5] AS sampleMembers
ORDER BY size DESC
LIMIT 10
Tells WCC to read the collaborations property as the relationship weight
Only connections where actors collaborated more than 5 times are considered — this breaks the giant component into smaller, more meaningful groups of frequent collaborators
With threshold: 5.0, only connections where actors shared more than 2 movies are considered. This breaks the giant component into smaller, more meaningful groups of frequent collaborators.
Seeded Components
What happens when new data arrives daily? For billion-node graphs, full recomputation is expensive. Seeded WCC lets you build incrementally.
The idea: store previous component IDs, then only recompute for new or changed nodes.
Seeding: Step 1 — Project with Seed Property
The first time we ran WCC on the Movies graph, we wrote the `componentId`s to the graph.
Now, let’s include existing `componentId`s in our projection:
Includes the previously written componentId as a node property in the projection — WCC will use these as starting assignments instead of treating every node as a new singleton
