Opinion Propagation Over Social Networks:Modeling And Analysis

Modeling and analysis of propagation processes has attracted great interest of many researchers due to its wide range of applications in various fields,such as biology,economics,and social science.At present,most studies of propagation problem focus on the network with only cooperative interactions.Generally,the propagation of opinion is affected by the type of interaction between individuals.This thesis focuses on modeling and analysis of opinion propagating over signed networks.The signed network can be used to effectively characterize both cooperative(trustful/friendly)and antagonistic(distrustful/hostile)interactions among individuals in a social network.The main results and contributions include the following points.1.The propagation problem of multiple competing opinions over signed networks is studied.The individual will either stick to his/her own previous opinion with a certain probability or randomly select one of neighbors to determine his/her opinion.If the individual selects a neighbor interacting with his/her in a cooperative way,he/she adopts the neighbor's opinion.While for the antagonistic interaction,the individual adopts one opinion from the multiple competing opinions subtracting the neighbor's opinion in non-uniform and uniform probability,respectively.According to the update rules established above,we provide two propagation models.For the non-uniform scenario,a new network is constructed and its connection with the signed network is illuminated.Taking advantage of this connection,we give a sufficient condition for the propagation model to converge.For the uniform scenario,we present necessary and sufficient conditions in terms of network topology,which ensure the convergence of the propagation model.Moreover,if the signed network is structurally balanced,we find that the probabilities for individuals in different subgroups to adopt the same opinion are complementary.2.We study a competitive problem between two stubborn individuals in a signed network,that is,they try to maximize the expected number of non-stubborn individuals adopting their opinions.Two stubborn individuals hold two competing opinions and never change their opinions,and the non-stubborn individual can change his/her own opinion.The stubborn individual propagates his/her opinion in the signed network by selecting some nonstubborn individuals to connect to.The payoff of each stubborn individual is denoted by the expected number of non-stubborn individuals adopting his/her opinion.This competitive problem is formulated into a two-player zero-sum game,where players are the two stubborn individuals.Firstly,for the zero-sum game,we give the necessary and sufficient condition for the existence of pure-strategy Nash equilibria.Secondly,the signed network with the structurally balanced property is further considered.We find that when two stubborn individuals connect to non-stubborn individuals belonging to different subgroups,the payoff of each stubborn individual is equal to the number of non-stubborn individuals in a subgroup.For the signed cycle network,we present a necessary and sufficient condition to determine whether a strategy profile is a Nash equilibrium.Finally,we show that the stubborn individual can increase his/her payoff by connecting to suitable non-stubborn individuals.3.We consider the case that two competing opinions propagate over signed networks,and each individual changes his/her opinion in a manner similar to being “infected” by a disease.If the interaction between the individual and his/her neighbor is cooperative,he/she believes the opinion of his/her neighbor.While for the antagonistic interaction,the individual believes the opposite opinion.Based on the above rule and the susceptible-infectedsusceptible model over networks,a novel propagation model is proposed.As in the majority of the work on the epidemic spreading,this propagation model also shows a threshold phenomenon.Firstly,we give a threshold condition such that the zero equilibrium of the propagation model is asymptotically stable.Actually,this means that if the threshold condition is satisfied,the opinions will eventually disappear in the network.Secondly,we show that if the threshold condition is violated,the nonzero equilibrium is existent.Moreover,the influences of the structurally balanced and unbalanced signed networks on the propagation process of opinions are analysed.