Skip to content
Contact us
  • There are no suggestions because the search field is empty.

Expert Guides for Navigating Complex Business Networks

Learn. Analyze. Optimize.

Table of contents

Quick Start Guide

RedGraphs Guide: Interpreting Network Analytics

2nd February 2025

Network Analytics and Interpretation

Network analysis relies on centrality to measure a node’s importance based on its connections. Centrality can represent social status, infrastructure significance, or a company’s strength in an economy. The four key centrality measures are:

  • Degree – Number of direct connections.
  • Betweenness – Role in connecting different parts of the network.
  • Closeness – Proximity to all other nodes.
  • Eigenvector/Power – Influence based on connected nodes’ importance.

These metrics are widely used in social network analysis and have emerging applications in Business Relationship Analytics for evaluating companies, sectors, and economies.

Degree Centrality

A measure of a company’s customer and supplier power

Definition

Degree centrality measures a company’s customer and supplier power based on its network connections. It is divided into:

• In-degree – Number of incoming links (customer demand).

• Out-degree – Number of outgoing links (supplier dependencies).

For directed networks, the formula is:

Cd(v)=deg⁡(v)n-1

where weights can adjust for connection strength. This metric is computed in O(E) time for sparse graphs and is typically scaled between 0-1 for clarity.

Interpretation

• In-degree centrality represents supplier power—a company with many high-value inbound connections has strong pricing leverage.

• Out-degree centrality represents customer power—a company with diverse, high-value outbound connections can negotiate better terms.

Customer and Supplier Power in Business Networks

In business, in-degree and out-degree help assess customer and supplier power:

• A company with many high-value inbound connections (diverse revenue streams) is a strong supplier with significant pricing power—especially if its customers have fewer, weaker outbound links.

• A company with many high-value outbound connections (diverse cost streams) is a strong customer, gaining leverage over suppliers, particularly if those suppliers have weaker inbound connections.

Extreme Cases:

• A monopolist holds high supplier power, being the sole seller.

• A monopsonist has high customer power, being the sole buyer.

While these scenarios concentrate power, they also drive innovation as markets seek alternatives. Degree centrality analysis can reveal which companies are gaining or losing influence in their supply chains.

Learn more
Degree Centrality

Betweenness Centrality

A Key Indicator of Market Bottlenecks

Definition

Betweenness centrality measures how often a company or entity acts as a bridge in a network by appearing in the shortest paths between other entities. The formula is:

where:

• n_{st} = Total shortest paths between nodes s and t .

• n_{st}(v) = Shortest paths that pass through vertex v .

Betweenness is computed using Johnson’s algorithm for sparse graphs in O(V² log V + VE) time and is typically normalized between 0 and 1 for easy interpretation.

Interpretation

Betweenness centrality identifies bottlenecks—entities that control the flow of resources, information, or transactions.

• Social Networks: A high-betweenness person acts as a bridge between disconnected groups (e.g., a negotiator or mediator).

• Business & Supply Chains: A high-betweenness company sits at a critical junction, with most suppliers selling to it and most customers buying from it—giving it both customer and supplier power.

Real-World Examples

• International Olympic Committee (IOC) – The IOC holds exclusive power over the buying of athletic performances and selling of Olympic broadcasting rights, making it a high-betweenness entity.

• Strategic Supply Chain Players – A logistics hub or a key supplier in an industry may hold a dominant position by controlling crucial flow points.

Use Cases for Betweenness Analysis

• Market Power Analysis – Identifies companies controlling industry bottlenecks.

• Supply Chain Optimization – Reveals vulnerabilities where disruptions could impact multiple players.

• Competitive Intelligence – Tracks how power shifts over time within an industry.

By analyzing betweenness centrality, businesses can identify dominant market players, predict industry shifts, and assess risks related to supply chain dependencies.

Learn more
betweenness-1

Closeness Centrality

A Measure of Economic Integration

Definition

Closeness centrality measures how directly a company connects to others in an economic network. It is calculated as the mean weighted shortest path from one entity to all others, prioritizing companies that are well-integrated. The formula is:

where d_G(v, t) is the shortest path distance, and lower values indicate higher closeness. This metric is computed using Johnson’s algorithm for sparse graphs in O(V² log V + VE) time and is typically normalized between 0 and 1.

Interpretation

• Social Networks: High closeness means a person is well-connected and aware of network-wide changes, even if they don’t control information flow.

• Business & Economy: A company with high closeness is deeply embedded in the economy, meaning:

• It is quickly impacted by market shifts.

• Its actions influence many other businesses.

• It can serve as an indicator of systemic economic health.

Use Cases for Closeness Analysis

• Economic Indicators – Companies with high closeness can signal market trends.

• Systemic Risk – Firms with high closeness may pose more significant financial risks.

• Market Sensitivity – Closeness can be compared to Beta to assess stock volatility.

By tracking closeness centrality, businesses and investors can identify key economic players and predict shifts in financial markets.

Learn more
closeness-1

Eigenvector Centrality

Measuring Economic Influence

Definition

Eigenvector centrality measures a company’s importance in the economy by considering both direct and indirect connections. Unlike simple connectivity measures, it assigns higher scores to companies linked to other high-scoring companies, reflecting global influence rather than just local interactions.

It is calculated using:

where A is the network matrix, \lambda is an eigenvalue, and x represents centrality scores. The Perron-Frobenius theorem ensures a stable dominant eigenvector for ranking companies.

Google’s PageRank and early search engine algorithms were built on variations of this concept. The HITS algorithm refined it by distinguishing between hubs (aggregators of information) and authorities (trusted sources).

How It Works in Business

Eigenvector centrality models how money flows through an economy by stabilizing dead ends in the network:

• Supply Chains: If a company has no suppliers, feedback loops are preserved by restarting the flow at another point.

• Economic Sectors: If an entire sector absorbs resources without supplying back, small adjustments ensure realistic modeling.

Interpretation

• Social Networks: A person is important if they are connected to other important people.

• Business Networks: A company is critical if it supplies or interacts with other high-impact companies.

• Economic Health Indicator: Eigenvector centrality reflects the global economic influence of a business, capturing systemic risk and market equilibrium states.

Use Cases for Eigenvector Centrality

• Market Influence – Identify key players shaping industries.

• Systemic Risk – Assess businesses that could trigger financial disruptions.

• Alpha Generation – Analyze long-term shifts in economic influence for investment insights.

By tracking eigenvector centrality, businesses and investors can predict economic shifts, identify influential companies, and improve market forecasting.

Learn more
eigenvector-1