Stochastic Actor-Based Models for Network Local-Dynamics

Network Analysis or Social Network Analysis (SNA) is a set of methods that allows to study relational structures between a set of actors that should be companies, people, countries, web pages and so on. Considering for instance a criminal organization, studying money transfer and/or communication between its members is possible to understand who are the bosses, who are the intermediares, who are the soldiers, who are the clients and providers and how to work the whole organization. A network is given by the union of a mathematical structure called graph and the data. Data are not only classic attributes on individuals but also relational data that express some type of relation between the actors. Network analysis was introduced by Moreno (1934) in social studies, at the beginnig it was only a descriptive-deterministic method but afterwards Wasserman, Holland and others introduced also probabilistic evaluation on networks.
The aim of this thesis is to give an introduction to the Network Analysis and to deal with local- dynamics over time of a network. In particular, considering evolutive networks using stochastic actor-oriented models developed by Tom A.B. Snijders in 1996, these are simulation based models. In these models, each actor can choose an action about creation and termination of its outgoing ties, this choice is based on actor’s network perception and relationship with its alters, attributes and other features. The actor takes the choice that maximizes its own aims that are represented by a linear function of structural effects and attributes. Estimation procedures are based on Monte Carlo Markov Chain simulation method. The analysis of this models allows to find which are the factors that influence the choice of an actor to change the state of a relation with an alter but they are not able to give a global description of the evolution of the network, in this sense they are models for local-dynamics.