Claviro

Graph Basics

Node Degree & Centrality

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Understanding Graph Basics

Key Concepts
  • Nodes: Vertices that represent entities
  • Edges: Connections between nodes
  • Density: Measure of how connected a graph is
  • Degree: Number of edges connected to a node
Density Formula

Degree(v) = |\{u : (u,v) \in E\}|

About this concept

What to notice

Nodes with high degree have many connections and often play important roles in the network.

Why it matters

Centrality measures help identify influential nodes in social networks, communication networks, and organizational hierarchies.

Think about

Who is the most connected person in your social network? What does that tell you about their influence?

Formula & Application

Key Formula

Degree(v) = |\{u : (u,v) \in E\}|

Use this formula to calculate the relationship between different variables in this concept.

Example

In a citation network, a highly cited paper has high degree centrality.