A network is a collection of points, called nodes, connected by lines, called edges. This structure can represent anything from a group of friends on social media to interconnected airports. Within these systems, some nodes are more important than others. The method used to measure the influence of a single node within the network is called centrality analysis.
This analysis identifies significant nodes, such as influential people or major transportation hubs. The concept was developed within social network analysis to understand the roles individuals play within social structures. Examining a node’s position helps us understand its function and influence on the rest of the network.
Degree Centrality
Degree centrality measures a node’s importance by counting its number of direct connections, or edges. In a social network, a person with the most followers has the highest degree centrality. This metric is straightforward because it only requires information about a node’s immediate connections.
A high degree centrality suggests a hub of activity with numerous direct links, allowing for the rapid dissemination of information. For instance, a journalist with many direct contacts can spread a story widely. Conversely, a node with low degree centrality is on the periphery of the network with less immediate influence.
This measurement is local, as it does not consider the network’s global structure. Its limitation is that it treats every connection as equal and does not account for the importance of the nodes to which it is connected.
Betweenness Centrality
Betweenness centrality measures a node’s influence by its role as a bridge. It identifies nodes that frequently lie on the shortest paths connecting other pairs of nodes. A node with high betweenness acts as a connector, controlling the flow of information between different parts of the network, making them gatekeepers.
In an international airport system, a major hub like Dubai connects passengers traveling between smaller, disconnected cities. This airport has a high betweenness centrality because it is a link in many travel itineraries, and removing it could disrupt connections across the network.
This measure shows that a node does not need many direct connections to be important. A bridge connecting two islands has low degree centrality but high betweenness centrality. In organizations, individuals in these bridging positions can become informational bottlenecks or brokers.
Closeness Centrality
Closeness centrality measures a node’s importance by its accessibility to all other nodes. It calculates the average shortest path length from one node to every other node. Nodes with high closeness centrality can reach the rest of the network most efficiently, spreading information with minimal delay.
When planning a new emergency facility like a hospital, placing it at a location with high closeness centrality minimizes average travel time to any point in the city. This ensures the fastest possible response. Similarly, a server with high closeness can distribute data to all client machines with the lowest latency.
This measure focuses on the speed of dissemination across the entire network, providing a global perspective on a node’s position. A node is central if it can quickly interact with all other nodes. This makes it a useful metric for identifying optimal points for distribution.
Eigenvector Centrality
Eigenvector centrality operates on the principle that not all connections are equal. A node’s importance is determined by the importance of its neighbors. A node connected to other influential nodes will have a higher eigenvector centrality than one connected to many less important nodes.
The adage, “it’s not what you know, it’s who you know,” captures this concept. In a professional network, a connection to a single industry leader is more valuable than connections to many interns, as the leader’s connection confers more influence.
A well-known application is Google’s PageRank algorithm, a variant of eigenvector centrality. A webpage is considered important if linked to by other important webpages. This method improved web search by providing results based on the quality of links, not just the quantity.
Applications of Node Centrality
Centrality measures are tools for analyzing networks in various fields. In epidemiology, betweenness centrality helps identify potential “super-spreaders.” It pinpoints individuals who act as bridges between communities, which can facilitate the transmission of a disease across separate groups.
In marketing, degree centrality can find individuals with the largest immediate audience for broad campaigns. For campaigns targeting specific influential circles, eigenvector centrality is more effective because it identifies individuals whose endorsements carry more weight.
For infrastructure planning, closeness centrality helps find the optimal location for a new facility, like a distribution center. It identifies the location with the most efficient access to the population. In counter-terrorism, analysts use betweenness centrality to disrupt covert networks by identifying brokers who control the flow of information between cells.