Here are the main parameters you can configure when running Betweenness Centrality:
Parameter
Default
Description
writeProperty
(required)
Property name for storing results
samplingSize
all nodes
Number of source nodes for approximation
samplingSeed
random
Seed for reproducible sampling
Exact versus approximate
By default, Betweenness computes exact results using all nodes as sources.
For large graphs, you can use sampling to get approximate results much faster. We’ll look at this option later in the lesson.
Finding bridge papers
With Betweenness scores written to the database, we can query for the top bridge papers.
python
Querying top bridge papers
q_top_betweenness = """
MATCH (p:Paper)
WHERE p.betweenness IS NOT NULL
RETURN
p.paper_Id AS paperId,
p.subject AS subject,
p.betweenness AS betweenness,
p.pageRank AS pageRank // (1)
ORDER BY p.betweenness DESC
LIMIT 10
"""
df_bridges = gds.run_cypher(q_top_betweenness) # (2)
display(df_bridges)
Including PageRank alongside Betweenness lets us compare influence vs connectivity for each paper
gds.run_cypher() returns results as a pandas DataFrame for easy analysis
Interpreting the results
Notice how the top papers by Betweenness are often different from the top papers by PageRank.
High Betweenness papers act as connectors between research communities. These are often methodological papers whose techniques apply across multiple domains.
Interpreting Betweenness scores
Betweenness scores are relative to your specific graph:
A score of zero means no shortest paths pass through this node (often leaf nodes)
Low scores indicate regular nodes with few paths passing through them
High scores indicate bridges or bottlenecks
You should only compare scores within the same graph. A score of 500 means very different things in different networks.
Comparing PageRank and Betweenness
Let’s visualise the relationship between influence (PageRank) and connectivity (Betweenness).
This helps us understand the different types of important papers in the network.
python
Querying papers with both metrics
q_both_metrics = """
MATCH (p:Paper)
WHERE p.pageRank IS NOT NULL
AND p.betweenness IS NOT NULL // (1)
RETURN p.pageRank AS pageRank,
p.betweenness AS betweenness,
p.subject AS subject
"""
df_metrics = gds.run_cypher(q_both_metrics)
Filtering for nodes with both metrics ensures we only compare papers that have been scored by both algorithms
Creating a scatter plot
Now we can create a scatter plot to see how the two metrics relate.
python
Creating a scatter plot of PageRank vs Betweenness
import matplotlib.pyplot as plt
plt.figure(figsize=(10, 6))
plt.scatter(df_metrics['pageRank'],
df_metrics['betweenness'],
alpha=0.5, s=10) # (1)
plt.xlabel('PageRank (Influence)')
plt.ylabel('Betweenness Centrality (Connectivity)') # (2)
plt.title('PageRank vs Betweenness in Citation Network')
plt.grid(True, alpha=0.3)
plt.show()
Low alpha and small point size prevent overplotting when thousands of papers overlap
Labeling axes with the metric interpretation (not just the name) helps readers understand the plot
Bottom-left: Regular papers
Most papers cluster in the bottom-left quadrant. These have low influence and low connectivity.
This is expected—the majority of papers in any network are not exceptional by either measure.
Top-right: Superstar papers
Papers in the top-right quadrant are both influential AND highly connected.
These are rare papers that are widely cited and also serve as bridges between research areas.
Top-left: Bridge papers
Papers in the top-left quadrant have high connectivity but moderate influence — none here.
These are true bridge papers—they connect different research areas even though they may not be the most famous works.
Bottom-right: Influential specialists
Papers in the bottom-right quadrant are influential but not strongly connecting different areas.
These are important papers within their specific field, but they don’t bridge to other research communities.
Combining algorithms reveals richer insights
Different algorithms reveal different types of importance in your network.
Using PageRank alone, you would miss the bridge papers. Using Betweenness alone, you would miss the influential specialists.
Combining them gives you a more complete picture.
Cross-subject bridge analysis
Let’s find out which research subjects produce the most bridge papers.
python
Analysing bridge papers by subject
q_subject_bridges = """
MATCH (p:Paper)
WHERE p.betweenness > 1000 // (1)
RETURN
p.subject AS subject,
count(p) AS num_bridge_papers,
avg(p.betweenness) AS avg_betweenness,
avg(p.pageRank) AS avg_pageRank // (2)
ORDER BY num_bridge_papers DESC
"""
df_subject_bridges = gds.run_cypher(q_subject_bridges)
display(df_subject_bridges)
Threshold of 1000 selects papers with meaningful bridge roles; adjust based on your graph’s score distribution
Including PageRank alongside Betweenness shows whether bridge subjects are also influential
Interpreting subject analysis
Subjects with many high-Betweenness papers tend to be methodological fields that influence multiple domains.
These are the research areas where techniques and ideas flow outward to other communities.
Table 1. Bridge Papers by Research Subject
subject
num_bridge_papers
avg_betweenness
avg_pageRank
Neural_Networks
401
11,854
1.24
Theory
206
12,227
1.37
Probabilistic_Methods
205
13,763
1.31
Genetic_Algorithms
188
14,365
1.45
Case_Based
159
9,407
1.24
Reinforcement_Learning
108
13,188
1.44
Rule_Learning
73
6,838
1.22
Finding specific cross-subject bridges
We can also find papers that specifically cite across multiple different research areas.
These are the truly interdisciplinary works.
Querying cross-subject bridges
This query finds papers with high Betweenness that cite at least three different subjects.
python
Finding papers that bridge multiple research areas
q_cross_subject = """
MATCH (p:Paper)-[:CITES]->(cited:Paper)
WHERE p.betweenness > 500
AND p.subject <> cited.subject // (1)
WITH p,
collect(DISTINCT cited.subject) AS cited_subjects,
count(DISTINCT cited.subject) AS num_subjects_cited
WHERE num_subjects_cited >= 3 // (2)
RETURN
p.paper_Id AS paperId,
p.subject AS subject,
p.betweenness AS betweenness,
p.pageRank AS pageRank,
num_subjects_cited,
cited_subjects // (3)
ORDER BY num_subjects_cited DESC, p.betweenness DESC
LIMIT 10
"""
df_cross_subject = gds.run_cypher(q_cross_subject)
pp(df_cross_subject)
Filters to cross-subject citations only, ignoring within-field references
Requires at least 3 different subjects cited — true interdisciplinary breadth
Returns the list of cited subjects so you can see exactly which fields each paper bridges
Truly interdisciplinary papers
These papers have both structural importance (high Betweenness) and actually cite work from three or more different fields.
They serve as knowledge transfer hubs, synthesising ideas from across the research landscape.
Uses only 500 source nodes instead of all 2,708 — trades accuracy for speed on large graphs
Fixed seed ensures reproducible results across runs
Comparing exact and sampled results
You can compare exact and sampled results to see how close the approximation is.
python
Comparing exact vs sampled Betweenness
q_compare = """
MATCH (p:Paper)
WHERE p.betweenness IS NOT NULL
AND p.betweenness_sampled IS NOT NULL // (1)
RETURN p.paper_Id AS paperId,
p.betweenness AS exact,
p.betweenness_sampled AS sampled
ORDER BY p.betweenness DESC // (2)
LIMIT 10
"""
df_compare = gds.run_cypher(q_compare)
display(df_compare)
Both properties must exist to compare — only papers scored by both runs are included
Ordering by exact scores lets you check whether the top bridges are preserved by sampling
Compare sampled vs unsampled results
Table 3. Top 10 papers: Exact vs Sampled Betweenness
paperId
exact
sampled
35
850,663
135,989
3229
460,318
84,396
4330
324,663
67,198
1365
310,253
69,272
6213
278,922
57,619
887
247,254
54,440
1272
230,426
35,196
910
193,210
34,932
3231
182,882
32,799
6214
149,405
29,118
When to use sampling
Consider using sampling when:
Your graph has millions of nodes
Exact computation takes too long for your use case
Approximate results are acceptable for your analysis
For the Cora dataset with 2,708 nodes, exact computation is fast enough that sampling isn’t necessary.
On larger graphs, sampling can significantly reduce computation time while still identifying the most important bridge nodes.
Performance considerations
Betweenness is more expensive than PageRank for a few reasons:
It computes shortest paths between many node pairs
Memory usage increases with the level of parallelism
Undirected graphs are more expensive than directed graphs
Handling memory issues
If you run into memory problems on large graphs, you can:
Reduce the concurrency parameter to use fewer parallel threads
Use samplingSize to compute approximate results
Consider whether you need exact Betweenness or if another centrality measure would suffice
Disconnected graphs
Betweenness only counts paths that actually exist in the graph.
If your graph has isolated components, nodes may have zero Betweenness even if they are central within their own component.
Betweenness relativity
A Betweenness score of 5000 means nothing without context.
You should only compare scores within the same graph.
The same score in a different network would have a completely different meaning.
Common pitfall: Expecting similarity to PageRank
High PageRank does not imply high Betweenness, and vice versa.
They measure fundamentally different things: Influence versus connectivity.
Summary
Betweenness Centrality identifies bridges and bottlenecks in your network:
It measures how often a node lies on shortest paths between other nodes
High-Betweenness nodes are connectors that link different parts of the network
It complements PageRank by revealing a different type of importance: Connectivity rather than influence
For large graphs, use the samplingSize parameter to get approximate results faster
Always compare scores within the same graph, never across different networks
You’ve now used both PageRank and Betweenness to analyse the citation network, finding both influential papers and bridge papers.
Next: Use Louvain community detection to discover research clusters in the network.
