Graph sampling by lagged random walk

TL;DR

This paper introduces lagged random walk sampling methods for graphs, where transitions depend on current and previous nodes, enabling estimation of various subgraph-based parameters with improved flexibility.

Contribution

It presents a novel family of lagged random walk sampling techniques that generalize existing methods and allow estimation of complex subgraph features at equilibrium.

Findings

Incorporates existing random walk methods as special cases.

Enables estimation of parameters related to edges, triangles, and cycles.

Provides a new approach for subgraph-based graph analysis.

Abstract

We propose a family of lagged random walk sampling methods in simple undirected graphs, where transition to the next state (i.e. node) depends on both the current and previous states -- hence, lagged. The existing random walk sampling methods can be incorporated as special cases. We develop a novel approach to estimation based on lagged random walks at equilibrium, where the target parameter can be any function of values associated with finite-order subgraphs, such as edge, triangle, 4-cycle and others.