I recently completed a project studying networks and including the quantitative measures that help define influence and connection. The concept can seem abstract, like nodes, edges, clusters, and centrality scores. These terms felt like they were pulled from computer science rather than something I could apply in real-world analysis. After spending a few weeks on a use case, I gained something from the project and wanted to share the fundamental ideas that I found helpful in network analysis.
What Are Networks, Nodes, and Edges?
A network is simply a collection of objects and the connections between them. Those objects are called nodes, and the connections are called edges.
In a social network, nodes might be people, and edges represent friendships or follows. In an ecological network, nodes can be species, and edges represent the food chain relationships between them. In a business network, companies are nodes, and partnerships, transactions, or digital interactions form the edges that connect them.
Edges can be directed (showing a one-way flow of information, such as one company following another on X) or undirected (representing a mutual relationship, like a collaboration). They can also be weighted, meaning that some connections carry more strength or frequency than others, or unweighted, where all connections are treated equally.
Quantitative Metrics: How Networks Are Measured
Understanding a network involves quantifying its structure. Tools like Gephi, an open-source software for network visualization and analysis, make this process approachable. Gephi can compute network-wide metrics and node-level measures that describe how influence and information flow through the system.
Here are some of the most useful concepts to know:
Degree Centrality
This is the simplest measure — it counts how many connections a node has.
- In-degree measures the number of edges pointing toward a node (i.e.,how many others connect to it). Below is an example of ranking Fortune 500 companies by in-degree within a network of other Fortune 500 companies.
- Out-degree measures how many edges point away from it (how many others it connects to).
| Rank | Company | In-Degree | Followers | Following |
| 1 | Ford Motor Co. | 61 | 1,132,486 | 31,371 |
| 2 | General Electric | 58 | 455,315 | 14,105 |
| 3 | Starbucks Coffee | 54 | 11,569,681 | 96,843 |
| 4 | Microsoft | 54 | 8,468,612 | 2,564 |
| 5 | 50 | 13,649,140 | 702 | |
| 6 | Home Depot | 48 | 377,035 | 32,274 |
| 7 | General Motors | 43 | 666,669 | 6,312 |
| 8 | Intel | 42 | 4,803,776 | 1,267 |
| 9 | Boeing | 42 | 485,654 | 243 |
| 10 | Cisco | 41 | 651,735 | 3,207 |
In a social network, a node with high in-degree is popular or influential, while a node with high out-degree is active or outwardly engaged.
Betweenness Centrality
This metric highlights the bridges in a network, which are the nodes that connect otherwise separate groups. A node with high betweenness lies along the shortest paths between others. These nodes play critical roles in linking communities and enabling information to spread across boundaries.
Eigenvector Centrality
While degree counts connections, eigenvector centrality weighs the quality of those connections. A node has a high eigenvector score if it’s connected to other important or well-connected nodes. This is often seen as a measure of prestige or embeddedness that influences by association rather than sheer popularity.
| Rank | Company | Eigenvector |
| 1 | Starbucks | 1.000 |
| 2 | Ford Motor Co. | 0.923 |
| 3 | Southwest Airlines | 0.898 |
| 4 | 0.836 | |
| 5 | Home Depot | 0.819 |
| 6 | Microsoft | 0.787 |
| 7 | JetBlue Airways | 0.759 |
| 8 | American Express | 0.687 |
| 9 | General Electric | 0.680 |
| 10 | PepsiCo | 0.660 |
Closeness Centrality
This metric measures how close a node is to all others in the network. A node with high closeness can quickly reach or be reached by others. In practical terms, these are efficient communicators — well-positioned to access or spread information quickly.
PageRank
Originally designed by Google to rank web pages, PageRank is similar to eigenvector centrality but adds a probability-based weighting. It measures the likelihood that a random “walk” through the network would land on a given node, favoring nodes that are frequently linked to by other central nodes. In social or business contexts, it represents visibility and authority.
| Twitter Name | PageRank | In-Degree | Eigenvector Centrality |
| Starbucks Coffee | 0.01761429 | 54 | 1 |
| 0.0158226 | 50 | 0.836416998 | |
| General Electric | 0.01545142 | 58 | 0.679982027 |
| Microsoft | 0.01348358 | 54 | 0.787053632 |
| AT&T | 0.01294237 | 39 | 0.589781765 |
| JetBlue Airways | 0.01250298 | 33 | 0.75860999 |
| Entertainment Tonight | 0.01186054 | 9 | 0.120362424 |
| Southwest Airlines | 0.01174446 | 37 | 0.897564724 |
| Ford Motor Company | 0.01167814 | 61 | 0.922857216 |
| Netflix US | 0.01122636 | 11 | 0.320554121 |
Modularity
While the measures above describe individual nodes, modularity is about the overall community structure of the network. It detects clusters of nodes that are more connected to each other than to the rest of the network. High modularity indicates distinct communities. For instance, clusters of technology companies, financial institutions, or consumer brands that interact more within their group than outside it.
Interpreting Networks: What the Numbers Mean
Quantitative metrics give structure to the complexity of relationships. For example, in a social media network of corporations, a company with a high in-degree might be a trendsetter whose posts attract widespread attention. A company with high betweenness might bridge industries by connecting technology firms with consumer brands. Meanwhile, a firm with high eigenvector or PageRank scores could represent a respected voice with strong reputational ties to other influential entities.
These measures together help analysts identify influencers, bridges, and communities, offering a deeper understanding of how ideas, influence, and collaboration circulate.
Using Gephi to Explore Networks
One of the best tools for exploring these ideas hands-on is Gephi. It’s open-source, free to use, and allows you to import data from spreadsheets or APIs. Once loaded, you can visualize nodes and edges, run algorithms like modularity or PageRank, and even color or size nodes based on their metrics. The visual aspect often reveals patterns that raw numbers can’t like clusters of interaction, isolated nodes, or cross-community bridges.
For researchers, educators, and data enthusiasts alike, Gephi provides an accessible entry point into network science. You can use it to study corporate relationships, social media patterns, trade flows, or ecological systems. The same fundamental principles apply: nodes and edges form a structure, and that structure tells a story.