Centrality

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Within graph theory and network analysis, there are various measures of the centrality of a vertex within a graph that determine the relative importance of a vertex within the graph (for example, how important a person is within a social network, or, in the theory of space syntax, how important a room is within a building or how well-used a road is within an urban network).

In other words, the centrality of a node in a network is a measure of the structural importance of the node. These measures attempt to quantify the prominence of an individual actor embedded in a network. A central actor, presumably, has a stronger influence on other network members.

The measures include:

• Degree
• Betweenness
• Closeness
• Eigenvector centrality
• Flow centrality (see Network flow)

The actors can also be aggregated to obtain a group-level centrality indices. For example, centralization refers to the extent to which the network is concentrated on one actor or a group of actors. Empirically, a centralized network is one which has few nodes (or just one) with considerably higher centrality scores than others in the network (e.g. a large variability of individual centrality scores).