This paper introduces a class of models for social network analysis based on latent positions in an unobserved "social space." The models assume that the probability of a relationship between actors depends on their positions in this space. The authors propose methods for inferring these latent positions and the effects of observed covariates using maximum likelihood and Bayesian frameworks, along with Markov chain Monte Carlo (MCMC) procedures. They analyze three standard datasets from social network literature and compare their method to a stochastic blockmodeling approach. The latent position model provides a visual and interpretable spatial representation of social relationships and allows for quantifying and graphically representing statistical uncertainty in the social space. The paper discusses two main types of models: distance models and projection models. Distance models assume that the probability of a tie depends on the Euclidean distance between actors in social space, while projection models consider the angle between actors' characteristics. Both models allow for probabilistic transitivity in network relations. The authors also discuss estimation methods, including MCMC techniques for inferring latent positions and parameters. They highlight the advantages of their approach, including flexibility, the ability to handle missing data, and the potential for generalization to multiple relationships and time-varying relations. The authors apply their models to three datasets: the Monk data, the Florentine families data, and the classroom data. In each case, the latent position model provides a better fit than alternative models, and the results are easier to interpret. The models also allow for the identification of clusters of individuals with similar social characteristics and the quantification of the extent to which some actors lie between other groups. The paper concludes that the latent position model is a promising approach for social network analysis, offering a more flexible and interpretable alternative to traditional models.This paper introduces a class of models for social network analysis based on latent positions in an unobserved "social space." The models assume that the probability of a relationship between actors depends on their positions in this space. The authors propose methods for inferring these latent positions and the effects of observed covariates using maximum likelihood and Bayesian frameworks, along with Markov chain Monte Carlo (MCMC) procedures. They analyze three standard datasets from social network literature and compare their method to a stochastic blockmodeling approach. The latent position model provides a visual and interpretable spatial representation of social relationships and allows for quantifying and graphically representing statistical uncertainty in the social space. The paper discusses two main types of models: distance models and projection models. Distance models assume that the probability of a tie depends on the Euclidean distance between actors in social space, while projection models consider the angle between actors' characteristics. Both models allow for probabilistic transitivity in network relations. The authors also discuss estimation methods, including MCMC techniques for inferring latent positions and parameters. They highlight the advantages of their approach, including flexibility, the ability to handle missing data, and the potential for generalization to multiple relationships and time-varying relations. The authors apply their models to three datasets: the Monk data, the Florentine families data, and the classroom data. In each case, the latent position model provides a better fit than alternative models, and the results are easier to interpret. The models also allow for the identification of clusters of individuals with similar social characteristics and the quantification of the extent to which some actors lie between other groups. The paper concludes that the latent position model is a promising approach for social network analysis, offering a more flexible and interpretable alternative to traditional models.