Eigenvector Centrality

Eigenvector Centrality

Eigenvector Centrality | Network Encyclopedia 

What is an Eigenvector Centrality?

Eigenvector Centrality measures the influence of a node in a network by considering not just the number of its connections, but also the importance of the nodes it is connected to. Nodes that are connected to other highly central nodes will have higher Eigenvector Centrality scores, making it an effective measure for identifying influential players in a network.

This centrality is calculated using the eigenvectors of the adjacency matrix of the network, which reflects how influence propagates through the connections.

An Example of Eigenvector Centrality

In a professional network, consider a consultant who interacts with a few influential executives (who themselves are highly connected to other key players). Despite having relatively few connections, the consultant's connections to powerful nodes result in a high Eigenvector Centrality score, signifying their indirect influence within the network.

Why Use a Spring Layout?

Eigenvector Centrality provides a nuanced view of influence by factoring in the quality of a node’s connections:
  1. Identifies Key Influencers: Nodes with high scores are often pivotal to the network’s structure and flow of information.
  2. Highlights Strategic Connections: It emphasizes the importance of being connected to other influential nodes, rather than just having many connections.
  3. Improves Decision-Making: Organizations can identify stakeholders whose positions in the network make them effective leaders, communicators, or resources for collaboration.

How is Eigenvector Centrality Different from Other Measures?

Unlike Degree Centrality, which counts the number of direct connections, Eigenvector Centrality accounts for the connections' significance. It also differs from Betweenness Centrality, which focuses on the role of nodes as intermediaries rather than their network influence.

When to Use Eigenvector Centrality?

This metric is particularly valuable in networks where influence spreads through prominent nodes, such as social media networks, collaboration networks, or leadership ecosystems. It’s often used in scenarios where leveraging influence can amplify outcomes, such as viral marketing or coalition building.


    • Related Articles

    • Closeness Centrality

      Closeness Centrality | Network Encyclopedia What is Closeness Centrality? Closeness Centrality measures how close a node is to all other nodes in the network, based on the shortest paths. A node with high Closeness Centrality has shorter average ...

    • Social Network Analysis

      Social Network Analysis | Network Encyclopedia What is Social Network Analysis? Social Network Analysis (SNA) is a methodological approach used to understand the structures and patterns of relationships within a network. It examines how nodes ...

    • Betweenness Centrality

      Betweenness Centrality | Network Encyclopedia What is Betweenness Centrality? Betweenness Centrality measures how often a node lies on the shortest paths between other nodes in a network. It quantifies the extent to which a node acts as a bridge or ...

    • Unimodal Network

      Unimodal Network | Network Encyclopedia What is a Unimodal Network? A Unimodal Network is a network where all nodes represent the same type of entity. These networks focus on homogeneous relationships, such as friendships, collaborations, or ...

    • Graph Theory

      Graph Theory | Network Encyclopedia What is Graph Theory? Graph Theory is the mathematical study of graphs, structures that model relationships between pairs of objects. Graphs are composed of nodes (vertices), representing entities, and edges ...