| Περίληψη : | Social networks have become a huge interdisciplinary research area with important links to sociology, economics, epidemiology, computer science, and mathematics. A flurry of numerous articles, notably the influential and recent books shows the growing relevance of this field. It deals with such diverse topics as epidemics, spread of certain patterns of social behavior, effects of advertising, and emergence of ‘bubbles’ in financial markets.A large part of research on social networks focusses on the problem of diffusion that is the spread of a certain event or information over the network, for example becoming infected or adopting a given product.A social network is a graph of relationships and interactions within a group of individuals and plays a fundamental role as a medium for the spread of information, ideas, and influence among its members. An idea or innovation will appear for example, in the use of cell phones among college students, in the adoption of a new drug within the medical profession, or in the rise of a political movement in an unstable society and it can either die out quickly or make significant inroads into the population.If we want to understand the extent to which such ideas are adopted, it can be important to understand how the dynamics of adoption are likely to unfold within the underlying social network: the extent to which people are likely to be affected by decisions of their friends and colleagues, or the extent to which “word-of-mouth” effects will take hold. Such network diffusion processes have a long history of study in the social sciences.Many researches have been done focusing on data pertaining to the adoption of medical and agricultural innovations in both developed and developing parts of the world; in other contexts, research has investigated diffusion processes for “word-of-mouth” and “viral marketing” effects in the success of new products and the sudden and widespread adoption of various strategies in game theoretic settings.In this research we are going to present an overview of the algorithmic diffusion models that have been proposed during the last decades in the literature for the adoption of a single product. Moreover we will focus our attention in the influence maximization problem which has been studied from many different researchers in many papers and it is the most interesting part from algorithmic and marketing aspect.After that we are going to present some results from simulation tests that have been done with the use of a tool that has been created as a part of this study. Finally we are going to present some models for the spread of multiple products over a social network. This topic is still under research in the academic community and only a few models have been proposed up to now. In this area we are going focus on a game theoretic analysis of a competitive diffusion process.
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