Centrality Measures on Complex Networks
Complex systems, in general, can be represented as networks, where the units of the system become nodes and interacting units are connected by edges. Several researches showed that many networks are characterized by a heterogeneous distribution of the number of neighbors of a node, or degree, where nodes with low degree coexist with nodes
with large degree (hubs). The presence of nodes with different degrees means that there is a broad diversification of their roles within the graph. Centrality measures are designed to rank graph nodes based on their topological importance.
Among the most popular centrality measures we mention degree itself, but also measures
depending on shortest paths between nodes’ pairs, like
node betweenness and closeness. There are as well centrality measures that depend on spectral properties of graph matrices. These measures are important because
they are usually associated to simple dynamic processes on graphs, like diffusion and their evaluation can be related to well known problems in Physics.
The application of these type of measure is crucial in many fields such for example: search engines, campaigns of vaccinations, control of power grids, discovery of important proteins etc..
with large degree (hubs). The presence of nodes with different degrees means that there is a broad diversification of their roles within the graph. Centrality measures are designed to rank graph nodes based on their topological importance.
Among the most popular centrality measures we mention degree itself, but also measures
depending on shortest paths between nodes’ pairs, like
node betweenness and closeness. There are as well centrality measures that depend on spectral properties of graph matrices. These measures are important because
they are usually associated to simple dynamic processes on graphs, like diffusion and their evaluation can be related to well known problems in Physics.
The application of these type of measure is crucial in many fields such for example: search engines, campaigns of vaccinations, control of power grids, discovery of important proteins etc..
