How Works Degree Centrality?
The most simple and popular centrality measurement is the degree centrality. How and why different types of degree centrality can be calculated.
Degree undirected network
Nieminen introduced in 1974 the network measurement degree centrality in an undirected network [1]. This centrality counts the number of neighbours of a node, walks with length of one.
The degree can be interpreted as the probability to capture as a node whatever flows through the network, such as a virus or information. In a social network the degree centrality can be used to find nodes with many direct friendships and is often considered a measure of activity, e.g. Facebook. Nodes with a low degree are not active, peripheral members of the network.
Degree directed network
In a directed network we have 2 measures of degree centrality, this was introduced in 1979 by Freeman [3]:
- in-degree centrality or degree prestige: number of INcoming arrows to a node;
- out-degree centrality: number of OUTgoing arrows to other nodes.
In a social network the arrows represent the communication, e.g. Instagram. The largest the in-degree the more prestigious and followers the account has. The out-degree is often seen as a form of activity or gregariousness.
Degree weighted network
You can calculate degree centrality with weighted networks as well. In that case, the sum of weights of all neighbour edges is the degree.
Adjacency network
Another representation of the network is shown in the adjacency matrix. It is easier to calculate with a matrix. The degree of a node is now the sum of the values in a row or column.
Degree normalisation
If we compare networks and a node (n) has a degree of 9, is it important? This depends, if a high-density network has 11 nodes: yes, it is important: 9 out of 10 potential edges (n-1). But if there are 101 nodes, the node is not important, 9 out of 100 edges.
That's why you need to normalise centrality scores; divide score by the maximum possible edges. If we do not allow a link between a node and itself, this is n - 1. This places all scores in the range of 0 to 1. A node with a normalised degree of 1 is connected to all nodes in the network. Now networks have the same scale and can be compared.
Pro degree centrality
Compared to other centrality measures, degree centrality is the simplest to calculate, you don't need to know the total network to calculate.
Con degree centrality
The degree of a node only measures locally; it doesn't really tell us where the node is in the network. A node with a high degree centrality can be far out from the core of the network, the periphery of a network.
Conclusion
The type of network determines how to calculate degree centrality. If you want to compare networks, you need to normalise centrality scores. The degree centrality is perhaps the most simple and popular, but in most cases, there is another centrality that fits better.
References
[1] Nieminen, J. (1974). On the centrality in a graph. Scandinavian journal of psychology, 15(1), 332-336.
[2] 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.
[3] Freeman, L. C. (1978). Centrality in social networks conceptual clarification. Social networks, 1(3), 215-239.