Flooding in weighted sparse random graphs of active and passive nodes

TL;DR

This paper models flooding in large weighted sparse random graphs with active and passive nodes, providing an approximation for typical flooding times relevant to information spread and epidemic containment.

Contribution

It introduces a new model incorporating active and passive nodes with exponential weights, offering an approximation formula for flooding time in such graphs.

Findings

Derived an approximation formula for flooding time

Applicable to models of information spread and epidemics

Analyzed the impact of node types on flooding dynamics

Abstract

This paper discusses first passage percolation and flooding on large weighted sparse random graphs with two types of nodes: active and passive nodes. In mathematical physics passive nodes can be interpreted as closed gates where fluid flow or water cannot pass through and active nodes can be interpreted as open gates where water may keep flowing further. The model of this paper has many applications in real life, for example, information spreading, where passive nodes are interpreted as passive receivers who may read messages but do not respond to them. In the epidemic context passive nodes may be interpreted as individuals who self-isolate themselves after having a disease to stop spreading the disease any further. When all weights on edges between active nodes and between active and passive nodes are independent and exponentially distributed (but not necessary identically distributed), this article provides an approximation formula for the weighted typical flooding time.