In this work; three specific dynamical systems models, the Basic, Maki-Thompson, and Daley-Kendall, are used to model rumor transmission on social networks. Rumor flow is a measure of the time it takes for the rumor to completely pass through a specified network. Comparisons between random social networks and a small world social networks yield the faster transmission of a rumor over a small world network.
Using unique adjacency matrices that define our random networks, observations of some characteristics of the random networks will be made that are specific to this type of graph. Differences in the constructs of the two networks will be illustrated by comparing these properties to those of the small world networks (created by a certain rewiring scheme of a k-regular network). Interesting comparisons are to be made about the networks\u27 defining characteristics include average clustering coefficients, centrality measures, and average path lengths. The flow of a rumor through each type of network reveals the characteristics of the network. A rumor will clearly flow through a small world network faster than in a random network, mainly due to higher density, increased clustering and better defined centrality
