What is Betweenness Centrality?

This video explains how and why different types of betweenness centrality can be calculated and includes exercises to practice this. The video also discusses an important assumption.

BETWEENNESS UNDIRECTED NETWORK
Centrality is a common measure in network analysis, but it’s often poorly understood. A popular centrality measurement is the betweenness centrality, this centrality attempts to capture the role of nodes as a bridge between other groups of nodes.
To determine the betweenness centrality, we must first list the unique pairs of nodes of a network. Betweenness centrality uses the geodesic distance or shortest paths between all pairs of nodes in a network to calculate the bridgeness. The shortest path between two nodes goes through the fewest links. Now we can calculate the betweenness centrality.
1. Calculate unique pairs of nodes of a network
2. Determine shortest paths (geodesic distance) of these pairs
3. Calculate fraction shortest paths that pass through a node
4. Normalize
The video shows more details and an exercise to practice this.

MEANING BETWEENNESS CENTRALITY
For most centrality measurements, important means popular. Betweenness centrality captures a very different kind of importance: individuals controlling the flow around a network.
They are also the ones whose removal from the network will disrupt interactions the most.

BETWEENNESS NORMALISATION
If we want to compare networks of different sizes, we have to normalise the betweenness centrality score.
📽️ Normalisation vs standardisation 📏:    • Normalization vs Standardization  

ASSUMPTION BETWEENNESS
An important thing to keep in mind is that betweenness centrality is based on the shortest path and ignores other paths between nodes. In real life this is more complicated, and the chosen path is not always the shortest.

BETWEENNESS ALTERNATIVES
There are also variations on the betweenness centrality. Some relax the assumption by considering all possible paths. Alternatives are for instance: delta centrality, information centrality, random walk centrality, local clustering coefficient, stress centrality and percolation centrality

BETWEENNESS DIRECTED NETWORK
In practice, most use cases are directed networks, fortunately we can also calculate the betweenness centrality for these networks. Since this network is not symmetrical, there are a few minor differences with an undirected network. The video shows how to calculate this.

BETWEENNESS WEIGHTED NETWORK
You can calculate betweenness centrality with weighted networks as well. Now not all distances between nodes are the same. Instead of the shortest path we now take the minimal weighted path.

PROS and CONS
👍 Entire network: A major advantage of betweenness is that the position of a node is related to the whole network
👍 Flow perspective: this is a different kind of importance compared to other centralities.
👎 Assumption shortest path: In real life, a flow doesn't always take the shortest path.
👎 Calculation time: Calculating of the betweenness centrality can take a lot of time in a huge network.
👎 Use with care: a bridge can also be on the periphery of the network and this centrality is also sensitive to changes in the network.

CONCLUSION
Betweenness centrality measures another, and in most cases interesting property of nodes in a network. This may be why it is a popular centrality.

ℹ️ 🔗 What is betweenness centrality? https://symbio6.nl/en/blog/analysis/b...

TIMESTAMPS
0:00 Betweenness centrality
0:29 Betweenness undirected network
0:36 Exercise: calculate all pair of nodes
1:51 Meaning betweenness centrality
2:13 Visualisation
2:29 Normalisation
3:10 Exercise: calculate betweenness
3:52 Assumption shortest path
4:08 Alternatives
4:18 Betweenness directed network
4:40 Betweenness weighted network
4:58 Pros and cons betweenness centrality
5:40 Conclusion

VIDEOS IN THIS SERIES 🎞️
📽️ Centrality: Data Set vs Network    • Видео  
📽️ What is Network Centrality?    • What is Network Centrality?  
📽️ Why Network Analysis 🤔🧐:    • Видео  
📽️ Ways to Visualise a Network 🤔👁️🧐😃:    • Видео  
📽️ How Symbio6 Improves Your Business 🤝📈🤩:    • Видео  

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CONTRIBUTIONS

Music: Scott Holmes Music - New Beginnings

Vignery, K., & Laurier, W. (2020). A methodology and theoretical taxonomy for centrality measures: What are the best centrality indicators for student networks?. PLoS One, 15(12), e0244377.