Graph sampling by lagged random walk

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.

Graph spatial sampling

“…The LMHW (1) generalises the lagged random walk (LRW) proposed by Zhang (2021) where u i ≡ 1, i.e. without the MH mechanism.…”