Closeness Centrality
Closeness Centrality (Bavelas-Freeman Shortest-Path Measure) · Also known as: closeness, farness-based centrality, geodesic closeness, normalized closeness centrality
Closeness centrality measures how quickly a node can reach all others in a network by computing the inverse of its average shortest-path distance to every other node. First described by Bavelas (1950) and formally unified by Freeman (1979), it identifies nodes that can spread information or resources efficiently across the entire graph — not merely nodes with many direct contacts.
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When to use it
Use closeness centrality when you want to identify nodes that can most efficiently broadcast information, mobilize resources, or access the rest of the network with minimal intermediaries — for example, locating optimal diffusion seeds, influential communicators, or transit hubs. It is appropriate for connected or near-connected graphs of any size. Do not use it as the primary centrality measure when the network is highly fragmented (many disconnected components), because raw closeness scores become near-zero and meaningless; apply Wasserman-Faust normalization or analyze components separately. Avoid confusing closeness with degree: a node can have many direct ties yet still be peripheral in global reach.
Strengths & limitations
- Captures global reachability rather than just local connectivity, making it ideal for studying information flow and diffusion.
- Normalized score (0 to 1) enables comparison across networks of different sizes.
- Well-established theoretical foundation with decades of validation in sociology, epidemiology, and computer science.
- Complements degree and betweenness centrality to give a richer picture of node roles.
- Efficiently computable with BFS (unweighted) or Dijkstra (weighted) for most empirical networks.
- Sensitive to graph connectivity: in disconnected networks the raw measure collapses and requires normalization adjustments.
- Treats all shortest paths as equally important; does not account for the volume of traffic or the probability that a specific path is actually used.
- Computationally expensive on very large graphs (millions of nodes) because all-pairs shortest-path computation scales poorly without approximation algorithms.
- Does not distinguish between a node that is close to many weak ties versus one close to a few strong, strategically important ties.
Frequently asked
How does closeness differ from degree centrality?
Degree centrality counts only direct neighbors, so a node can score high if it has many connections even if those connections are all clustered in one corner of the network. Closeness considers the shortest path to every node in the graph, so it rewards global reachability. A peripheral clique hub may have high degree but low closeness.
What should I do when my network has disconnected components?
Apply the Wasserman-Faust (1994) harmonic or reachability-adjusted normalization, which sums only reachable pairs and rescales by the proportion of the network reachable. Alternatively, analyze the largest connected component separately, or use harmonic centrality (the sum of reciprocal distances), which naturally handles unreachable pairs by assigning them a contribution of zero.
Does closeness work on weighted networks?
Yes. Replace BFS with Dijkstra's algorithm using edge weights as distances (or the inverse of strength/similarity weights if higher weight means closer). The resulting weighted closeness reflects both the topology and the quality of connections.
How do I interpret the normalized closeness score?
A score close to 1 means the node can reach every other node in roughly one hop on average — it sits at the center of the network. A score near 0 means the node is very peripheral. Scores above about 0.6 typically indicate genuinely central positions in most empirical networks.
Is closeness appropriate for directed networks?
Yes, but compute it separately in each direction. In-closeness measures how easily others can reach the focal node (useful for studying node prestige or receptivity), while out-closeness measures how easily the focal node can reach others (useful for studying broadcasting capacity).
Sources
- Freeman, L. C. (1979). Centrality in social networks: Conceptual clarification. Social Networks, 1(3), 215–239. DOI: 10.1016/0378-8733(78)90021-7 ↗
- Bavelas, A. (1950). Communication patterns in task-oriented groups. Journal of the Acoustical Society of America, 22(6), 725–730. DOI: 10.1121/1.1906679 ↗
How to cite this page
ScholarGate. (2026, June 3). Closeness Centrality (Bavelas-Freeman Shortest-Path Measure). ScholarGate. https://scholargate.app/en/network-analysis/closeness-centrality
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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- Degree CentralityNetwork analysis↔ compare
- Eigenvector CentralityNetwork analysis↔ compare
- Network Diffusion AnalysisNetwork analysis↔ compare
- PageRankNetwork analysis↔ compare
- Social Network AnalysisNetwork analysis↔ compare