Dynamic Monopolies in Colored Tori

Abstract

The {\em information diffusion} has been modeled as the spread of an information within a group through a process of social influence, where the diffusion is driven by the so called {\em influential network}. Such a process, which has been intensively studied under the name of {\em viral marketing}, has the goal to select an initial good set of individuals that will promote a new idea (or message) by spreading the "rumor" within the entire social network through the word-of-mouth.\ud Several studies used the {\em linear threshold model} where the group is represented by a graph, nodes have two possible states (active, non-active), and the threshold triggering the adoption (activation) of a new idea to a node is given by the number of the active neighbors.\ud \ud The problem of detecting in a graph the presence of the minimal number of nodes that will be able to activate the entire network is called {\em target set selection} (TSS). In this paper we extend TSS by allowing nodes to have more than two colors.\ud The multicolored version of the TSS can be described as follows: let $G$ be a torus where every node is assigned a color from a finite set of colors. At each local time step, each node can recolor itself, depending on the local configurations, with the color held by the majority of its neighbors.\ud \ud We study the initial distributions of colors leading the system to a monochromatic configuration of color $k$, focusing on the minimum number of initial $k$-colored nodes. We conclude the paper by providing the time complexity to achieve the monochromatic configuration

Opinion dynamics on interacting networks: media competition and social influence

“…The debate about social relevant issues spreads and persists over the web by leading to the emergence of unprecedented social phenomena such as the massive recruitment of people around common interests, ideas or political visions 9 10 11 12 . In the past years an intensive research effort has been payed in understanding social phenomena from innovation diffusion, to social influence, up to opinions and their dynamics 13 14 15 16 17 18 19 20 21 22 23 ; some of them have focused on the role of media 24 25 26 27 28 29 30 31 and of the web 32 33 .…”

Opinions Manipulation: Media, Power and Gossip

“…The WAs effect is relevant when the global tolerance is fixed to 2: the 30% of WAs is sufficient to invert the effect on mass opinions of the 70% of TWs. Furthermore when tolerance is higher (5), the number of WAs needed to inhibit media is smaller (20%). One may expect that tolerance plays a fundamental role in opinions' convergence toward the media or the WAs values.…”

Multi-level dynamo and opinion spreading

“…This challenge however is in general difficult due to the NP-hardness results (Kempe et al 2003). Different updating rules could also be investigated: for instance, in Brunetti et al (2011) the authors consider a different model, where a node updates its weight with the weight of the majority of its neighbours. Furthermore, in Ugander (2012) it was observed that the number of connected components in an individual's contact neighbourhood (representing separate social contexts for the user) is more influential than the size of the neighbourhood itself.…”