In the interest of nuance, it's important to note that, while the pigs hold a position of leadership within the farm, they're not entirely a unified bloc. Indeed, a major theme in the early part of Animal Farm is the conflict between Snowball and Napoleon for control of the farm. Snowball himself, as Napoleon's great opponent, is depicted as courageous (given his exploits in the Battle of the Cowshed) and, by all accounts, appears well intentioned. To this we must add the example of Major himself, the founder of Animalism, with his ideals of animal equality. Looking beyond the major personalities, you have the additional example of the four young pigs who raise opposition to Napoleon's dictatorial ambitions, only to be forcibly silenced and eventually executed, representing the purges in Stalinist Russia. That being said, even from early in the book, we see the presence of corruption among the pigs, and their subversion of animalist principle. Consider the ending of chapter 2, with the disappearance of the milk.
That being said, taken collectively, the pigs can be understood as representing the Communist Party leaders and Bolshevik elites, with Napoleon himself representing Stalin. We have across the course of Animal Farm themes of corruption (memorably expressed through the pigs' taking on of increasingly anthropomorphic characteristics) as well as of misinformation and propaganda, along with dictatorship and the use of suppression. In all these respects, the pigs represent a betrayal of the Revolution's principles. Taken in the context of Orwell's allegory, they represent a powerful indictment, first of the Bolsheviks and then (through Napoleon and his collaborators) of the Stalinist regime.