One of the important measures of influence in a network is a measure of betweenness centrality. Unlike the measure of degree, which 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.
This is a great concept, which also has philosophical consequences and the ability to change the way you think about multiplicities and power dynamics that exists within.
For instance, a node may have a lot of connections but if the connections are all within one group, this particular node will not be as important to the network as another node, which has less connections but is better connected across the network to all the different communities within. Thanks to its position the node will act as a broker and will play an important role in propagating information through the whole network, be it a community of people or a knowledge base.
Read more about the technical aspects of betweenness centrality and see some examples on our support portal.