Some kids are loud, some are quiet, some are too sociable while some are happier playing alone. There are different characters and personalities for the little ones and usually, such differences are caused by the culture inside their own homes. More often, the kids adapt the personality of his or her mom.
If you are an introvert mom, then your kids will most likely grow up as introverts too. This is not a generalization but a fact for most kids. Some studies say that shyness, being one of the traits of an introvert, is inherited but not permanent.
I have been an introvert myself since I was young. It was as intense as I get teary eyed whenever a person approaches me to ask something or talk to me. I am most affected by my teachers. I have just three close friends but most of the time, I enjoy myself alone in the house. My dad is an introvert and my mom is the more sociable one. I was such an introvert until I finished college. The change in environment changed my social being and developed my social skills. I am the opposite of who I am before. I can socialize with any person of any age from toddlers to senior citizens. I still am introvert at some degree but it is totally balanced now. I do not fear people anymore unlike before. I would agree that being an introvert is inherited but not permanent.
For some parents who are introverts, they find it a problem for their kids to socialize since their kids seem to inherit their own personality. I suppose this is not a huge problem at all. The kids can adjust later when the environment is changed or when they grow a little older.
The most important thing for the first seven years of a kid is to develop good values with them. Aristotle said that such period in a kid's life is very crucial so it is very essential that you put great attention on how the kids should grow. Anything that you teach him or her during this period will be brought by your kids until they get older.