In the context of graph theory and network science, betweenness centrality is an important measure of the node's influence within the whole network. While degree simply shows the number of connections a node has, betweenness centrality shows how often the node appears on the shortest path between any two randomly chosen nodes in a network (Brandes 2001).
Thus, betweenness centrality is a much better measure of influence because it takes the whole network into account, not only the local connectivity that the node belongs to.
In the context of text network analysis, the nodes with a high betweenness centrality serve as the 'crossroads' for the pathways of meaning or topical brokers, often linking the different contexts or topical clusters together. They may be the nodes are not only most frequently used, but also that occur at the narrative shifts, linking different topics in a text together.
In network visualization we often range the node sizes by their degree or betweenness centrality to indicate the most influential nodes (shown bigger on InfraNodus graphs).
These nodes with the highest betweenness centrality are shown in the Analytics > Essence > Most Influential Elements panel as well as the Insight > Topical Brokers panel.
Social Network Example: Betweenness Centrality and Influence
It may be easier to understand the notion of betweenness centrality using an example of a social network. In the context of social network analysis the nodes with the highest betweenness centrality are the people who tend to have not only a lot of connections, but also the highest level of diversity of those connections.
That is, you might know not so many people but if the people you know provide access to the diverse communities, then, given that there are no other people positioned better than you in the network, you'll have a high betweenness centrality.
For example, suppose we have a social network. There will be some nodes have fewer connections but higher betweenness centrality if they provide a pathway to the part of the community, which is unreachable otherwise. That is, a node may have high degree but low betweenness centrality. This indicates that it's well-connected within the cluster that it belongs to, but not so well connected to the rest of the nodes that belong to the other clusters within the network. Such nodes may have high local influence, but not globally over the whole network.
Alternatively, other nodes may have low degree but high betweenness centrality. Such nodes may have fewer connections, but the connections they do have are linking different groups and clusters together, making such nodes influential across the whole network. In fact, many efficient networkers and politicians will often trade some degree for betweenness centrality as it dramatically reduces their load while maintaining their central position within the network.
In the example above "Sean" is a node with a low betweenness centrality, while "You" has a high betweenness centrality. "You" is connected to all the different nodes within a group, except for Sean, while Sean is only connected to Mark. However, if Sean then makes links both to Sergey and to Larry in the first cluster, connects to Priscilla, and maintains his link to Mark , he will have higher betweenness centrality than You, because he connects all the different groups that exist within the network, even though You has more connections than Sean.