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Everything about Random graph

Graph generated by a random process

In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used to answer questions about the properties of typical graphs. Its practical applications are found in all areas in which complex networks need to be modeled – many random graph models are thus known, mirroring the diverse types of complex networks encountered in different areas. In a mathematical context, random graph refers almost exclusively to the Erdős–Rényi random graph model. In other contexts, any graph model may be referred to as a random graph. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Random graphA 5-minute orientation
  2. Skim a recent paper: Are Graph Convolutional Networks With Random Weights Feasible?Influential work since 2022
  3. Pick up a classic book: Random Graph DynamicsThe most-reprinted book on the subject
  4. Read the landmark paper: On random graphs. I.Cited 5,546 times
  5. Go sideways: Erdős–Rényi modelA closely related topic
  6. Go sideways: Giant componentA closely related topic

📖 Definitions

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🗂️ The subject at a glance

  1. Models
  2. Terminology
  3. Properties
  4. Colouring
  5. Random trees
  6. Conditional random graphs
  7. History

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics