Centrality in Networks: Finding the Most Important Nodes

Sergio Gómez

Abstract Real networks are heterogeneous structures,

with edges unevenly distributed among nodes,

presenting community structure, motifs, transitivity, rich

clubs, and other kinds of topological patterns.

Consequently, the roles played by nodes in a network

can differ greatly. For example, some nodes may be connectors

between parts of the network, others may be central

or peripheral, etc. The objective of this chapter is to describe

how we can find the most important nodes in networks.

The idea is to define a centrality measure for each node

in the network, sort the nodes according to their centralities,

and fix our attention to the first ranked nodes,

which can be considered as the most relevant ones

with respect to this centrality measure.