Sentiment cycles in discrete-time homogeneous networks

Abstract

h i g h l i g h t s• The paper approaches sentiment transition in a complex network.• Agents are classified in neutral, optimists and pessimists.• In continuous-time, the model delivers a stable steady-state outcome.• In discrete-time, stability holds under a homogeneous network of degree one.• Endogenous cycles emerge in discrete-time for a connectivity degree larger than one. a r t i c l e i n f o t r a c tConsider a network connecting individual agents that are endowed with distinct sentiments or 'views of the world'. Specifically, assume that each node in the network contains an agent that, at a given period t, can be found in one of five states: sentiment neutrality, exuberant optimism, non-exuberant optimism, exuberant pessimism and nonexuberant pessimism. Local interaction rules, similar to those one encounters in rumor propagation models, make agents change their sentiment as they contact with others. Under a continuous-time framework, the proposed setting delivers a stable fixed-point equilibrium, meaning that the shares of agents in each sentiment category will converge to constant steady-state levels. The inspection of the same structure of analysis in discretetime indicates that the stability outcome continues to hold when the connectivity degree is equal to 1. However, this result might change as one considers higher-order connectivity. In this last case, persistent endogenous waves of optimism and pessimism emerge under a reasonable parameterization of the model.

A model and simulation of the emotional contagion of netizens in the process of rumor refutation

“…Instead, they are undulating, fluctuating back and forth between minima and maxima in a negative or positive emotional wave 8 . As a subject’s emotional values fluctuate, the node may be infected by other people’s emotions 11 .…”

“…In recent years, some studies have begun to pay more attention to the impact of node attributes on the spread of rumors, such as the weight value of nodes 14 . In real social networks, the spread of rumors or emotions is not only related to the node state and the proportion of transition 11 but also to the individual’s inner emotional activity as the key factor to determine its transformation. Moreover, emotions affect the individual’s daily behavior as well as the information dissemination behavior of individuals.…”

“…This collective phenomenon has also been attributed to a large number of scattered microemotional interactions stemming from macroresults 10 . As a network structure with irregular and developing characteristics, the emotional contagion process is abstracted as the connection between network nodes and the change in state 11,12 .…”

Inferring Diffusion Network from Information Cascades using Transitive Influence

“…To study the behavior of people in a social network, the initial requirement is to infer the network structure from the observed data. Inferring the network structure of neurons in neuroscience [13], sentiment in online social networks [14], [15], community detection [16], or the genes in biology [17], [18] are similar points of interest in current researches. The aim of this article is investigating an epidemiology approach to infer the structure of an influence network from a set of information cascades, i.e., the time history of various events occurred in a network.…”

Sentiment Patterns

“…The obtained sentiment fluctuations mimic two important pieces of evidence: first, periods of generalized optimism alternate with periods of generalized pessimism and, second, each of the mentioned periods may persist for a relatively long time; these two features are commonly identified when assessing the short-term behavior of the most important macroeconomic variables. The structure of the model is adapted from Gomes [7], which in turn is inspired in the rumor propagation framework, as discussed by several authors [8][9][10] among many others. The fluctuations will emerge, in the present context, because we associate simple stochastic processes to the probabilities of transition across the considered sentiment states.…”