SAN FRANCISCO — Investors are clamoring to connect with the online networking service LinkedIn Corp. in the latest sign of the fervor for Internet companies that specialize in bringing together people with common interests.

The demand to buy a piece of LinkedIn is so intense that the eight-year-old company is expected to make its stock market debut Thursday with a value of at least $4 billion. That would make LinkedIn’s initial public offering of stock the biggest by a U.S. Internet company since Google Inc. went public in 2004.

The appetite for LinkedIn’s IPO encouraged the company’s bankers to raise the asking price by about 30 percent Tuesday to $42 to $45 per share. It won’t be surprising if the IPO is priced even higher this evening and then sells for more than that Thursday morning when they are expected to begin trading on the New York Stock Exchange under the symbol “LNKD.”

The IPO is expected to raise about $200 million for LinkedIn and produce $125 million to $135 million for existing stockholders. The biggest winner will be LinkedIn’s co-founder and chairman, Reid Hoffman, whose 20 percent stake in the company will be worth more than $800 million.

The coming-out party on Wall Street for LinkedIn, which focuses on connecting professionals online, could be the prelude to even more excitement if several popular Internet companies decide to go public during the next year. The list of candidates includes the online messaging service Twitter, online game maker Zynga, online coupon service Groupon and the biggest social network of all, Facebook.