Betweenness Centrality

Betweenness centrality measures how much a person or hub lies on the shortest routes connecting other pairs of nodes in a network. In the company example, Bob is the only link between two teams, so communication between them has to cross his position even though Alice has more contacts inside her team. Think of a toll booth on the only road connecting two towns: its position matters more than how many drivers the operator knows. Notice this: identify a connection between two teams, then check whether alternative routes exist before calling it a bottleneck.

Count routes rather than direct contacts

Degree counts a node's direct connections. Shortest-path betweenness instead considers routes between other pairs of nodes. For each pair, the measure counts the fraction of shortest routes that pass through the node, then adds these fractions across pairs. Different conventions may normalize the result, so comparisons need the same convention and network boundary.

See why a bridge can matter

If two groups have only one connecting node, that position can be a bottleneck for communication across the groups. A node need not have many direct contacts to occupy such a position. However, high betweenness does not by itself prove that removing a node will split the network: longer alternative routes may still connect it.

Specify the example's assumptions

Imagine two delegations that communicate only through one interpreter. In that hypothetical communication network, the interpreter lies on the routes between the delegations and can affect what is conveyed. If participants share another language or use other interpreters, the network and the conclusion can change. Having the job title 'translator' alone does not establish a high score.

Distinguish a measure from actual influence

A shortest-path score describes the chosen graph, not a complete model of human behavior. It can identify a potential gatekeeper or overloaded connection, but actual influence also depends on whether people use those routes, can find alternatives, and can act on the messages they receive.

Choose a flow model that fits

Information may spread along routes other than the shortest ones. Newman's random-walk measure is one alternative that gives credit to a broader range of paths. Use the metric that matches the question, and check how the result changes when the network boundary, links or routing assumptions change.

The conventional score adds, across pairs of other nodes, the fraction of their shortest paths that pass through a focal node; some conventions normalize this sum.

• Newman (2003 preprint) describes shortest-path betweenness, including fractional credit when a pair has several equally short paths, and relates it to potential influence over information flow. [1]
• The same paper develops a random-walk-based measure to include contributions from paths beyond the shortest ones, explicitly addressing the restrictive routing assumption of the conventional metric. [1]

A score depends on which nodes and links are included, how ties and weights are treated, and the chosen normalization. Shortest-path betweenness gives no guarantee that real traffic follows the counted routes, or that a high-scoring person actually controls communication. Longer bypasses can preserve connectivity even when a node carries many shortest paths. Computation becomes demanding on large graphs; its cost depends on the algorithm and graph properties, rather than one universal complexity for every implementation.