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Information Degradation and Misinformation in Gossip Networks

Thomas Jacob Maranzatto, Arunabh Srivastava, Sennur Ulukus

TL;DR

This work analyzes information quality in gossip networks where a source propagates updates and nodes overwrite with fresher packets. It introduces a Markov-degradation model for information quality and reduces the quality dynamics to a hopcount problem on a reversed auxiliary graph via a first-passage percolation framework. By specializing to a two-state misinformation process, it compares fully connected and ring graphs, showing the proportion of truthful information decays exponentially with age in both, but at different rates: $P(K_n)=p^{\Theta(\log n)}$ for the complete graph and $P(C_n)=p^{\Theta(\sqrt{n})}$ for the ring, with higher connectivity yielding slower misinformation spread. The paper conjectures exponential degradation across all gossip networks and posits that networks with better AoI would spread misinformation more slowly, highlighting a tradeoff between rapid information dissemination and information integrity.

Abstract

We study networks of gossiping users where a source observing a process sends updates to an underlying graph. Nodes in the graph update their neighbors randomly and nodes always accept packets that have newer information, thus attempting to minimize their age of information (AoI). We show that while gossiping reduces AoI, information can rapidly degrade in such a network. We model degradation by arbitrary discrete-time Markov chains on k states. As a packet is transmitted through the network it modifies its state according to the Markov chain. In the last section, we specialize the Markov chain to represent misinformation spread, and show that the rate of misinformation spread is proportional to the age of information in both the fully-connected graph and ring graph.

Information Degradation and Misinformation in Gossip Networks

TL;DR

This work analyzes information quality in gossip networks where a source propagates updates and nodes overwrite with fresher packets. It introduces a Markov-degradation model for information quality and reduces the quality dynamics to a hopcount problem on a reversed auxiliary graph via a first-passage percolation framework. By specializing to a two-state misinformation process, it compares fully connected and ring graphs, showing the proportion of truthful information decays exponentially with age in both, but at different rates: for the complete graph and for the ring, with higher connectivity yielding slower misinformation spread. The paper conjectures exponential degradation across all gossip networks and posits that networks with better AoI would spread misinformation more slowly, highlighting a tradeoff between rapid information dissemination and information integrity.

Abstract

We study networks of gossiping users where a source observing a process sends updates to an underlying graph. Nodes in the graph update their neighbors randomly and nodes always accept packets that have newer information, thus attempting to minimize their age of information (AoI). We show that while gossiping reduces AoI, information can rapidly degrade in such a network. We model degradation by arbitrary discrete-time Markov chains on k states. As a packet is transmitted through the network it modifies its state according to the Markov chain. In the last section, we specialize the Markov chain to represent misinformation spread, and show that the rate of misinformation spread is proportional to the age of information in both the fully-connected graph and ring graph.
Paper Structure (7 sections, 5 theorems, 17 equations, 2 figures, 1 table)

This paper contains 7 sections, 5 theorems, 17 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model and Preliminaries
  3. Age and Quality of Information
  4. Percolation and Hopcount
  5. Proof of Theorem \ref{['thm:general']}
  6. Misinformation: Comparison of $K_n$ and $C_n$
  7. Remarks

Key Result

Theorem 1

For every time $t$ and node $i$, the quality of information of $i$ at time $t$ has distribution given by

Figures (2)

  • Figure 1: A gossiping network with one source node generating and sharing updates. The nodes in the network share information with each other.
  • Figure 2: This figure shows the process of information degradation with time, which we follow with the transfer of a packet to nodes in the network starting from the source. The thinning of the red arrow represents the degradation of the packet being shared between nodes. In this gossiping network, the source sends an update to a node, represented by the red arrow coming from outside. This information is not degraded since it comes directly from the source, thus being represented by the thickest arrow. When this node shares information with the next node, there is information degradation, depending on the associated Markov chain.

Theorems & Definitions (5)

  • Theorem 1
  • Theorem 2: age_percolation
  • Theorem 3
  • Lemma 1
  • Theorem 4