Random Graphs

Erdős–Rényi model, phase transitions, and preferential attachment.

field tier

Random Graphs. Erdős–Rényi model, phase transitions, and preferential attachment.

Foundations and canonical references

The standard treatments of random graphs approach the subject from complementary angles. Bollobas, Random Graphs (2001) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Janson, Random Graphs (2000) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for random graphs include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 2001
    Random Graphs
    bollobas-2001
  • textbook · primary · 2000
    Random Graphs
    janson-2000, luczak-2000, rucinski-2000

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