Information Spreading in Random Graphs Evoving by Norros-Reittu Model

TL;DR

This paper analyzes how messages spread in a dynamic random graph model based on the Norros-Reittu preferential attachment, deriving probability distributions and success probabilities, supported by simulation results.

Contribution

It introduces a detailed probabilistic analysis of message dissemination in the Norros-Reittu evolving graph model, including distribution functions and success probabilities.

Findings

Derived probability mass functions for message spread and total nodes

Established the distribution of the ratio of informed to total nodes

Validated results through simulation studies

Abstract

The paper is devoted to the spreading of a message within the random graph evolving by the Norros-Reittu preferential attachment model. The latter model forms random Poissonian numbers of edges between newly added nodes and existing ones. For a pre-fixed time $T^*$, the probability mass functions of the number of nodes obtained the message and the total number of nodes in the graph, as well as the distribution function of their ratio are derived. To this end, the success probability to disseminate the message from the node with the message to the node without message is proved. The exposition is illustrated by the simulation study.