Degree Centrality in Network Theory
Definition 1
In a given network $G (V, E)$, the following is called Degree Centrality for each node $v \in V$. $$ \deg v $$
Description
Centrality
Centrality refers to the concept of ‘how important a node is within a given network’, and there are various definitions and methods of calculation depending on the problem of interest. Among many methods, the simplest is evaluating the degree itself as centrality, known as Degree Centrality.
The degree does not impart special meaning in just any graph without the value as data.
- For instance, in a network derived from SNS users as nodes and friendships as links, a ‘high degree of a node’ immediately indicates a ‘user with many friends’.
- An air network, with airports as nodes and airlines as links, is widely known to be a scale-free network, where a high degree means there are many direct flights to other airports, suggesting the importance of that airport.
It might seem like playing with words by merely attaching the term centrality to the degree, calculated by counting links, but without the assumption that a high degree itself can signify the importance of a node, one could question the validity of the logic that nodes such as hub nodes are essential. Fortunately, in many cases, nodes with a high degree are intuitively accepted as important.
While it has been stated that ’the degree does not impart special meaning in just any graph’, in fact, it’s even harder to find data among what we can access in which the degree isn’t important.
- As a rare example, like National Standard Node Link which uses intersections as nodes and roads linking them as links, the majority of degrees would typically be 3 or 4, hardly exceeding 6. Although the road network is a common and not particularly special example of a network, there’s a clear limit to analyzing it with degree centrality.
See Also
Various Centralities in Networks
Newman. (2010). Networks: An Introduction: p169. ↩︎