# Graph Database Solution for Higher Order Spatial Statistics in the Era of Big Data

## TL;DR

This paper introduces a graph database algorithm for efficiently computing higher-order spatial correlation functions in large point datasets, enabling practical analysis of galaxy distributions at cosmological scales.

## Contribution

The authors develop a novel graph-based algorithm utilizing kd-trees and graph databases to compute N-point correlation functions efficiently in big spatial data.

## Key findings

- Significant computational speed-up over traditional methods.
- Able to measure 3-point correlations beyond BAO scale in SDSS data.
- First measurement of 4-point correlation function in large galaxy sample.

## Abstract

We present an algorithm for the fast computation of the general $N$-point spatial correlation functions of any discrete point set embedded within an Euclidean space of $\mathbb{R}^n$. Utilizing the concepts of kd-trees and graph databases, we describe how to count all possible $N$-tuples in binned configurations within a given length scale, e.g. all pairs of points or all triplets of points with side lengths $<r_{max}$. Through bench-marking we show the computational advantage of our new graph based algorithm over more traditional methods. We show that all 3-point configurations up to and beyond the Baryon Acoustic Oscillation scale ($\sim$200 Mpc in physical units) can be performed on current SDSS data in reasonable time. Finally we present the first measurements of the 4-point correlation function of $\sim$0.5 million SDSS galaxies over the redshift range $0.43<z<0.7$.