See, the thing is, if the egg has been fertilized by a rooster, then the egg would be non-vegitarian because, in this case, the egg would hatch a new chick if a hen where to hatch it. Mostly, a hen most likely would hatch a fertilized egg. There's another case where a hen gives an egg that has not received fertilization from a rooster. In this case, the hen would not even try to hatch the egg. This egg would have no potential of giving birth to a new chick.
Vegetarianism is the practice of living solely upon vegetables, fruits, grains, and nuts.
Meat, fowl, and fish are excluded from all vegetarian diets, but some vegetarians use milk and milk by-products. However, the modern West usually includes eggs in their diet as well as milk and milk by-products. Vegetables in the broadest sense is any kind of plant life or plant product. Popularly, however, the term is restricted to the ripened ovaries that are sweet and either succulent or pulpy and that are usually eaten as an appetizer or a dessert. I trust this will clarify you query.