How Does Network Centrality Work?

What is Centrality?

Centrality can be calculated at different levels. Node centrality is the most used, it answers the network problem: what node in a network is important? The word important has a multitude of meanings, leading to many different definitions of centrality.

Why Centrality?

Why does network measurement centrality matter? Because networks are everywhere, and centrality gives us crucial information about these networks.

Node Centrality

The centrality of a node gives us an indication of the position of a node within the total network. In a social network, it is about identifying the most influential members. In a small network, centrality is often easy to see; in other networks, this is more difficult. The larger the network, the more challenging it is.

Many Node Centrality Definitions

There are many centrality definitions; the most simple and popular is degree centrality, which counts the number of neighbours of a node. In the video, we compare the four most commonly used definitions of centrality, each with its own meaning, pros and cons. Some node centrality measures:

• Neighbours based:
  • degree centrality (1)
  • eigenvector centrality (4)
  • authority and hub
  • Katz centrality
  • power centrality
  • PageRank
• Path based:
  • closeness centrality (3)
  • harmonic centrality
  • stress centrality
  • betweenness centrality (2)
  • information centrality
  • eccentricity

Network-Centrality

We can also measure centrality at the network level, also called centralisation. The idea of network centrality is to measure the overall centralisation of a network and refers to the properties of the network structure as a whole.

Centralisation does not refer to the relative importance of nodes, but to the overall coherence of a network. This is a descriptive statistic that summarises and organisese the characteristics of a network.

Which Centrality Should I Choose?

Most measures of centrality also come in many flavours, the choice depends on:

• problem and context
• level: network, group, node, or link
• network type: undirected, directed, weighted, and/or dynamic
• comparing networks: the centrality must then be normalised

Limitations

It is important to know that there are differences in the calculation of centrality between undirected, directed, and weighted networks. Each definition of centrality has its own meaning and could give different choices for the centre. Centrality measures are designed to identify the most influential nodes. For most other nodes, this ranking may be meaningless.

Conclusion

Is there a best centrality measurement? No, there is no best centrality measurement; carefully choose the centrality that best suits your business problem.