The Hegselmann-Krause system (HK system for short) is one of the most popular models for the dynamics of opinion formation in multi agent systems. Agents are modeled as points in opinion space, and at every time step, each agent moves to the mass center of all the agents within unit distance. The rate of convergence of HK systems has been the subject of several recent works and the current best bounds are O(n3) in one dimension and O(n4) in higher dimension where n being the number of agents. In this work, we investigate the convergence behavior of a few natural variations of the HK system and their e act on the dynamics. In the rest variation, we only allow pairs of agents who are friends in an underlying social network to communicate with each other and we can construct conjurations. In the second variation, only one of the agents updates its position at each time step and selection of such an agent may be at random or based on some preened order; as before, these updates of agents also take social information into consideration. In the third variant, agents may not move exactly to the mass center but somewhere close to it. In the fourth variant, we allow all agents to interact with one another, but instead of assigning equal weights to all neighbors as in the HK model, we assign Gaussian weights which are inversely proportional to the distance between agents. In the fifth variant, we consider the Synchronized Bounded In hence model where the agents have in hence bounds instead of con dance bounds, which changes the way agents interact with each other. In our nil variant, we consider the dynamics of HK systems with strategic agents where we have an additional set of agents called as strategic agents whose opinions are chosen freely at each time step. One of the goals using these strategic agents is to lower the convergence time. The dynamics of all the variants are qualitatively very different from that of the classical HK system. Nevertheless, we prove convergence or show some other interesting results for all of these models. To be more specific, for the rest and third variant we show that these systems make only polynomial number of non-trivial steps, regardless of the social network in the rest vary-ant and noise patterns in the third variant. For the second variant, however, we again show polynomial number of non-trivial steps but in expectation regardless of the social network and interestingly different dynamics. For the fourth variant, we prove an upper bound for the convergence time of Gaussian weighted HK model. For the fifth variant, we consider a special case of this SBI model and prove convergence for this case. For the final variant, we improve the existing results for the optimal convergence time for dumb-bell and equidistant configurations.

La dissémination d'information explore les chemins pris par l'information qui est transmise dans un réseau social, afin de comprendre et modéliser les relations entre les utilisateurs de ce réseau, ce qui permet une meilleur compréhension des relations humaines et leurs dynamique. Même si la priorité de ce travail soit théorique, en envisageant des aspects psychologiques et sociologiques des réseaux sociaux, les modèles de dissémination d'information sont aussi à la base de plusieurs applications concrètes, comme la maximisation d'influence, la prédication de liens, la découverte des noeuds influents, la détection des communautés, la détection des tendances, etc. Cette thèse est donc basée sur ces deux facettes de la dissémination d'information: nous développons d'abord des cadres théoriques mathématiquement solides pour étudier les relations entre les personnes et l'information, et dans un deuxième moment nous créons des outils responsables pour une exploration plus cohérente des liens cachés dans ces relations. Les outils théoriques développés ici sont les modèles de dynamique d'opinions et de dissémination d'information, où nous étudions le flot d'informations des utilisateurs dans les réseaux sociaux, et les outils pratiques développés ici sont un nouveau algorithme de détection de communautés et un nouveau algorithme de détection de tendances dans les réseaux sociaux / Our aim in this Ph. D. thesis is to study the diffusion of information as well as the opinion dynamics of users in social networks. Information diffusion models explore the paths taken by information being transmitted through a social network in order to understand and analyze the relationships between users in such network, leading to a better comprehension of human relations and dynamics. This thesis is based on both sides of information diffusion: first by developing mathematical theories and models to study the relationships between people and information, and in a second time by creating tools to better exploit the hidden patterns in these relationships. The theoretical tools developed in this thesis are opinion dynamics models and information diffusion models, where we study the information flow from users in social networks, and the practical tools developed in this thesis are a novel community detection algorithm and a novel trend detection algorithm. We start by introducing an opinion dynamics model in which agents interact with each other about several distinct opinions/contents. In our framework, agents do not exchange all their opinions with each other, they communicate about randomly chosen opinions at each time. We show, using stochastic approximation algorithms, that under mild assumptions this opinion dynamics algorithm converges as time increases, whose behavior is ruled by how users choose the opinions to broadcast at each time. We develop next a community detection algorithm which is a direct application of this opinion dynamics model: when agents broadcast the content they appreciate the most. Communities are thus formed, where they are defined as groups of users that appreciate mostly the same content. This algorithm, which is distributed by nature, has the remarkable property that the discovered communities can be studied from a solid mathematical standpoint. In addition to the theoretical advantage over heuristic community detection methods, the presented algorithm is able to accommodate weighted networks, parametric and nonparametric versions, with the discovery of overlapping communities a byproduct with no mathematical overhead. In a second part, we define a general framework to model information diffusion in social networks. The proposed framework takes into consideration not only the hidden interactions between users, but as well the interactions between contents and multiple social networks. It also accommodates dynamic networks and various temporal effects of the diffusion. This framework can be combined with topic modeling, for which several estimation techniques are derived, which are based on nonnegative tensor factorization techniques. Together with a dimensionality reduction argument, this techniques discover, in addition, the latent community structure of the users in the social networks. At last, we use one instance of the previous framework to develop a trend detection algorithm designed to find trendy topics in a social network. We take into consideration the interaction between users and topics, we formally define trendiness and derive trend indices for each topic being disseminated in the social network. These indices take into consideration the distance between the real broadcast intensity and the maximum expected broadcast intensity and the social network topology. The proposed trend detection algorithm uses stochastic control techniques in order calculate the trend indices, is fast and aggregates all the information of the broadcasts into a simple one-dimensional process, thus reducing its complexity and the quantity of necessary data to the detection. To the best of our knowledge, this is the first trend detection algorithm that is based solely on the individual performances of topics