Category: Statistics

Summary: Comparing critical thresholds and finite-size scaling exponents for percolation on Erdos-Renyi and Barabasi-Albert random graphs.

Percolation theory explains how global connectivity appears as edges are added, but finite systems do not jump at a single exact threshold. This experiment asks how the critical point and the width of the transition scale with graph size for two standard network families: Erdos-Renyi graphs and Barabasi-Albert preferential-attachment graphs.

The script measures the percolation transition across multiple graph sizes and estimates the finite-size scaling behavior, with special attention to the exponent governing the width of the critical window. It also treats the well-known Erdos-Renyi case as a validation benchmark while probing whether Barabasi-Albert graphs show measurably different scaling.

That matters because the Barabasi-Albert exponent is less settled than the classic Erdos-Renyi result. The experiment is designed to build a cleaner numerical comparison between a standard reference case and a more debated scale-free setting.

Method: Repeated bond-percolation simulations on Erdos-Renyi and Barabasi-Albert graphs, followed by finite-size scaling fits of the transition window.

What is measured: Critical threshold, finite-size scaling exponent, transition-window width, and differences between Erdos-Renyi and Barabasi-Albert graphs.