# What is the difference between local efficiency and betweenness centrality in network analysis?

There are many network properties that you can extract for a given node. Two I have encountered that sound conceptually very similar to me and that I have difficulty distinguishing are betweenness centrality and efficiency.

Definitions:

Betweenness: Node betweenness centrality is the fraction of all shortest paths in the network that contain a given node. Nodes with high values of betweenness centrality participate in a large number of shortest paths... measures the extent to which a vertex lies on paths between other vertices. Vertices with high betweenness may have considerable influence within a network by virtue of their control over information passing between others.

Local Efficiency: The global efficiency is the average inverse shortest path length in the network, and is inversely related to the characteristic path length. The local efficiency is the global efficiency computed on the neighborhood of the node, and is related to the clustering coefficient... quantifies the exchange of information across the whole network where information is concurrently exchanged.

To me, these sound quite similar, at least by their conceptual descriptions. Specifically, descriptions of both describe them as governing or controlling the exchange of information. But perhaps this is a time when the mathematical notation and understanding is necessary to understand the distinction.

Can anyone explain how these two network properties differ?