What Is Closeness Centrality?

Closeness centrality is a measure in network analysis that quantifies how close a node is to all other nodes in a network. The calculation is the inverse of the sum of the shortest path lengths between that node and all other nodes in the network. Closeness centrality identifies nodes that are important for efficient communication and information flow in a network and applies to various network types, such as social, transportation, and communication networks.

Closeness centrality definition

The idea that a node that is closer to all other nodes can more easily access and influence information in the network is what closeness centrality relates to. The closeness centrality of a node calculation is the inverse of the sum of the shortest path lengths between that node and all other nodes in the network. Essentially, it measures how quickly a node can reach all other nodes in the network and how quickly information can spread through the network as a result.

Who uses closeness centrality?

Since closeness centrality is a common measure utilized in network analysis, you will likely use this concept in network analytic roles. Individuals in network analyst roles often look to deploy the algorithm in cases where finding the most efficient or optimal path in a system is necessary. Telecommunication specialists looking to determine when information delivery will occur across a network may use closeness centrality to provide an estimate. Similarly, analysts of social networks can leverage closeness centrality to assess relationships between different people in a network and track how information is disseminated.

Network analysts play a crucial role in organizations across many industries by working to maximize the overall efficiency of network operations. As part of the IT team at their company, network analysts work hands-on with computer hardware and software and often serve as the individuals responsible for supporting and handling technical issues. Four common network analyst jobs in the workforce today are:

• Network engineer: Similar to a network administrator, network engineers play a key role in building and maintaining a company's IT system. They focus on designing systems that perform optimally and also focus on configuration, maintenance, and security within the system. 

• Network architect: Network architects focus on communication networks, leveraging their technical abilities to maintain and properly utilize the systems. They bridge the gap between software and hardware to promote network design, modeling, and security.  

• Network operations analyst: As part of the operations team within an IT department, network operations analysts work with various technical teams across an organization to handle any issues happening with the network system. They monitor, troubleshoot, and give technical support to resolve issues.

• Telecommunication specialist: Within communication systems, telecommunication specialists manage, build, and monitor overall performance, including finding new ways to improve the system's capabilities. They look to promote efficient interaction across all computers and devices included in the broader communication system.  

Read more: 4 Types of Neural Network Architecture

Closeness centrality examples

Closeness centrality identifies nodes that are important for efficient communication and information flow in a network. Some examples of closeness centrality include:

• Communication network: Closeness centrality identifies where the most important nodes for information dissemination are, such as websites or social media accounts that can quickly reach many people.

• Biological network: Closeness centrality identifies biological structures that play the most important roles in certain biological processes, such as pivotal genes, metabolites, or protein structures.

• Transportation network: Closeness centrality identifies exactly where the most central transportation hubs or stations are most easily accessible to all other locations in the network.

How do you calculate closeness centrality?

To calculate closeness centrality for a node, you first find the shortest path between that node and all other nodes in the network. Divide the sum of these distances by the total number of nodes in the network minus one (to account for the fact that the node itself is not included in the sum). The resulting score is the closeness centrality of the node. 

Harmonic centrality relates to closeness centrality and deals with unconnected nodes in a graph. Beauchamp introduced a new formula in 1965, where inaccessible distances become infinite by being zeroed out in the calculation [1]. An alternative way to look at this issue regarding closeness centrality came about almost 30 years later. In 1994, Wasser and Faust introduced a new and improved formula for closeness centrality to address any number of unconnected nodes present in a graph network [2].

Betweenness centrality vs. closeness centrality

Betweenness centrality is a measure in network analysis that identifies nodes with high communication flow and control over information flow. Betweenness centrality and the calculation of it does not have a standardized form. Various methods of calculation are sufficient in discovering betweenness. A basic example of the calculation is to take every network pair and count how often a “shortest path” between two nodes crosses this path. It measures how often a node occurs on all shortest paths between two nodes, and its value relates to the total number of shortest paths linking those two nodes.

Betweenness centrality calculates how much a given node is on the quickest path in between the other nodes. On the contrary, closeness centrality measures the closeness of a given node in comparison to all other nodes that exist in the network. Betweenness centrality is a measure of the node's importance for maintaining the connectivity of the network, while closeness centrality is a measure of how quickly information can spread through the network. Nodes with high betweenness centrality often become important for preventing network fragmentation, while nodes with high closeness centrality are important for information dissemination and efficient communication.

Getting started with Coursera

Closeness centrality is an important network analysis concept that allows you to determine the most influential nodes in a network. This is relevant across professional fields, helping professionals identify important biological pathways, information dissemination pathways, and transportation flow networks. 

If you’re interested in learning more about closeness centrality or network analysis in general, completing a course or receiving a relevant certificate is a great place to start. On Coursera, you can enroll in some of the top courses in the world.

To start, check out the Computational Social Science Specialization by the University of California, Davis. Taught at a beginner level, this Specialization examines social network analysis through case studies and discusses how networks become generated.

For more advanced material, check out  Applied Data Science with Python Specialization by the University of Michigan. This five-course series takes approximately four months to complete at 10 hours a week, and it offers flexible pacing so you can learn at your own speed.