The early American fiction writers Washington Irving, Nathaniel Hawthorne, and Edgar Allan Poe contributed significantly to the American literary canon with their unique styles of writing and their varied literary themes and forms. Analyze and research their literary works to support your thesis on the writing styles, themes, and forms of Irving, Hawthorne, and Poe. As you explore pertinent contexts, be careful to use appropriate literary, political, and cultural terminology in your writing.

One connection I see between Irving, Hawthorne, and Poe is a tradition of gothic themes and style in early American literature. It makes sense: the American colonists came to a "new" land, facing dangers they could not fully understand. They were in a strange place, with a physical landscape to learn and negotiate, but they also had to confront the native people of the land. It must have been frightening for both the colonists and the natives, but we are talking about European American writers. As a result, we see only their perspectives in the works of Irving, Hawthorne, and Poe. 
Gothic literature was a popular phenomenon in Europe in the 1700s and 1800s, though there are still works of literature published today that could be considered "gothic." Literature classified in the gothic genre is characterized by a fascination with the supernatural, the mysterious, the sublime, and the terrifying. This is interesting in the early American context because American gothic literature illuminated the dark side of life in a "new world." Of course, there was optimism and freedom, but there were also dangers and the unknown. Once the colonies began to unite and rebel against British rule, America itself entered the Age of Reason. The arguments for revolution and for the formation of a new nation were governed by the logic and rationality of the Enlightenment. At the same time, there was less patience for the fantastic, as people began to believe that science and reason could explain the phenomena of the world. The gothic, on the other hand, embraces the strangeness of the world, the things that cannot be explained or understood. 
Washington Irving is the earliest writer on your list, and he was living and writing in the aftermath of the American Revolution—the early years of the new nation. His two most famous works are "Rip Van Winkle" and "The Legend of Sleepy Hollow." The latter is obviously more in the gothic tradition, with the headless horseman and the obvious horror elements of that story. "Rip Van Wlnkle," though, also involves a supernatural element. There are the strange figures bowling and the fact that the lead character supposedly sleeps for twenty years. When he wakes up, he finds that his wife is dead and that the country is now a democracy. When he fell asleep, King George III was the ruler of the colonies. He finds that everything has changed around him, and it is certainly disconcerting; here, Irving comments on the sudden and profound changes wrought by the American Revolution. "Sleepy Hollow," again, is more obviously gothic in that its setting is supposedly haunted either by native spirits or by spirits who suffered traumatic deaths during colonial times. Ichabod Crane eventually comes face-to-face with the headless horseman and then leaves town mysteriously. There is some ambiguity at the end of story as to whether the headless horseman is real, but the story implies that it is actually a ghost. In summary, Irving's stories reflect on the tumultuous colonial times and the era of the young United States in a gothic style to highlight the darkness and the danger of early America.
Hawthorne and Poe are writing a bit later than Irving, aroundb the mid-1800s. This allows the writers to reflect on the early years of the nation in a less immediate way than Irving. Hawthorne had relatives who were involved in prosecuting "witches" during the famous Salem witch trials. The gothic themes that can be drawn from that history are obvious. Hawthorne's works tend to investigate the way early sins haunt the American environment throughout history. Hawthorne himself was haunted by his involvement in the trials; he even changed the spelling of his last name to distance himself from the family's heritage. Some of Hawthorne's most famous works are set in Puritan Massachusetts, even though the works themselves were published in the 1840s and 1850s. In The Scarlet Letter, for example, Hawthorne demonstrates the hypocrisy and extreme nature of Puritan theology. His most gothic work may be "Young Goodman Brown," a short story in which the title character travels into the woods at night on an important but mysterious errand, which eventually leads to a satanic ceremony. The story implies that all people in the community have gone through similar journeys. In other words, there is some sin and darkness in the heart of every person, even those who appear the most pious on the outside. Brown returns to the village the next day, and his life is forever ruined by what he has witnessed. It is a dark, ominous story that is definitely in the gothic tradition.
Poe is the most obviously gothic writer on this list, but he is also the least ostensibly political of the three writers. Poe is known for his ability to create a foreboding mood in works like "The Cask of Amontillado," "The Black Cat," and "The Fall of the House of Usher." While the final story is set in an old American home that collapses with the family line (an incestuous one, at that), Poe's stories take the gothic in a different direction; Poe's works are often about psychology. He is interested in madness and often uses unreliable narrators to explore the decline of a protagonist into insanity ("The Black Cat" is a textbook example). Poe's stories investigate the darkness in the human mind and heart, not just in the setting or political atmosphere. 
There are other ways to connect these three canonical early American writers, but, to me at least, the most interesting thread is the way the gothic tradition runs through each of these writers' works.