Call it The Washington Axiom: There are friends and there are friends. And since Washington is a town of friends, people who make a lot of them have a better chance of succeeding than people who don't.

Call him The Textbook Example: Ambassador Rinaldo Petrignani, 58, who in four years has moved Italy out of the also-rans of the diplomatic fast track into the Big Four of Embassy Row entertaining. (Great Britain and France are conceded to hold permanent membership, with opinion divided over which is fourth, Sweden or Canada.)

Call this The Price of Success: Hosting Friday's Opera Ball and four days later the Children's Hearing and Speech Center Barbecue, both with guest lists in the hundreds.

Worse things could happen to an ambassador whose goal is to wipe out stereotypes ("There are many things more interesting about Italy than Mafia," says Petrignani) so that Italy will rank right up there with Britain, West Germany and France when Americans think of Europe.

If American public opinion is not there yet, it hasn't been for Petrig-nani's lack of trying. In 1984 he and his Danish-born wife Anne Merete averaged 1.7 charity or community-related receptions, dinners, concerts and teas each week. Not included in that figure were the dozens of "political" dinners they hosted for Italian and American government officials.

"In terms of supporting local events, the Petrignanis really do their share," says Catherine Stevens, wife of Sen. Ted Stevens (R-Alaska) and chairman of this year's Opera Ball.

She describes how she, philanthropist David Lloyd Kreeger and Opera Society Women's Committee chairwoman Paula Jeffries, knowing that the Petrignanis also would be hosting the Speech and Hearing Center barbecue and Italy's national day around the same time, mustered up the courage to ask if they would host the ball.

"He has a great love for opera, especially Italian opera, and he's a great promoter of his country. But he kept us in suspense that day and we really didn't know if he'd do it or not," Catherine Stevens remembers.

"They never say no," says socialite-journalist Ina Ginsberg, often on the Petrignanis' guest lists.

"An ambassador has to establish a certain credibility, make himself known, become friends with those he has to deal with," says Petrignani, a career foreign service officer who was observing ambassadors at posts in New York, Washington, Geneva, Strasbourg, Brussels and Rome long before he became one in 1980. "I believe very much in personal connections."

Petrignani's personal connections reach everywhere into official and social Washington, some even beyond. By an accident of timing, one of the first Reagan officials he met when he arrived here in July 1981 was U.S. Chief of Protocol Lee Annenberg. She accompanied him to the White House when he presented his credentials to President Reagan.

Annenberg and her husband, multimillionaire publisher and former ambassador to Great Britain Walter Annenberg, were destined to become more than simply official friends of the Petrignanis.

"There is just something about them," says Lee Annenberg. "It comes and goes with different ambassadors -- I saw that in England. It depends on personality, how clever they are and how desirous they are to do a good job."

Petrignani is very desirous. "It is important that we should have access to the right people, that we should have the right connections, that we should cultivate personal and official friends," he said in a recent interview at Firenze House, the 59-room, 22-acre estate bordering Rock Creek Park that is the residence of Italy's ambassadors.

The Petrignanis' network of well-connected friendships, which might arouse envy in any diplomatic household, began to take shape soon after they met the Annenbergs. They included then-attorney general William French Smith; Nancy Reagan's good friend Betsy Bloomingdale; and the president's then-personal representative to the Vatican, William Wilson (now a full-fledged ambassador) and his wife Betty.

"We have come to know many of these exquisite people who are friends of the president," Petrignani readily admits. "We have been to their parties several times in Beverly Hills."

Among those was Jimmy and Gloria Stewart's 35th wedding anniversary party, and since Italy's foreign minister was in Los Angeles at the time, he was also invited to come along. Another Reagan intimate, Los Angeles industrialist Earle Jorgensen, and his wife Marion had the Petrignanis to dinner. And after the Petrignanis were house guests of the Annenbergs at Sunnylands, their desert oasis at Rancho Mirage, Frank and Barbara Sinatra, who live nearby, invited them to drop over.

The chance for the Petrignanis to reciprocate finally came in January when they invited their California friends, including the Sinatras, to dinner at the embassy and became Washington's hosts with the most social clout of inaugural week.

"At first it was casual," says Petrignani, who speaks as earnestly about socializing as he does about terrorism or missile deployment. "Now we have become good friends and I really cherish that, but I also know they are very good connections which can help me in my work."

Anne Petrignani, a tireless hostess, acknowledges that it all sounds so glamorous but it also is hard work. "It takes time to build up these connections. I thought there would be some quiet days, but the rings are getting bigger and bigger."

Even before Petrignani had presented his credentials at the White House, the fashion community in Washington, which had been all but ignored by Petrignani's bachelor predecessor, had trained its sights on the Italians' pseudo-Tudor mansion as a new fashion forum.

Within days of their arrival and still without their furniture, the Petrignanis agreed to open Firenze House for a Saks-Jandel fashion show. Single-handedly, the chef they brought with them from Brussels prepared dinner for 220. The party went on in a tent in the garden, with no one the wiser that the residence was almost bare.

"It was a good start. Many of the couples who came that night are still our friends," says Anne Merete Petrignani, who does her part for Italian fashion by wearing designs by Valentino and Laura Biagiotti. "My husband says Italy can sell itself. But I think nothing can really sell itself -- it has to be nourished."

Petrignani, continental in the old-fashioned hand-kissing sense ("and we don't get that from American men," sighs a Washington socialite), says parties set the stage for official business transacted later. Where it helps is in opening doors. "I don't want to abuse officials who are very busy, but I also know that whenever the need arises, I can knock at their doors and I will be received promptly."

The need arose earlier this spring when Italy's Prime Minister Bettino Craxi was coming to Washington for talks with Reagan. "In order to pull it all together," Petrignani says, "you have no idea how many people you have to talk with, how many contacts you have to have. If you know people, have access to them, it's much easier to get what you want and to get things done properly."

Among other demands made upon Italy's envoy was one that Craxi be invited to address a joint session of Congress. Congress prefers to reserve that honor for heads of state, not heads of governments. Not since Alcide de Gasperi came to town in 1951 had an Italian prime minister been invited to speak.

"It was a coup," says Sen. Larry Pressler (R-S.D.), a member of the Foreign Relations Committee, applauding Petrignani's quiet persistence that mobilized Italy's expanding domestic constituency into supportive action.

That's one aspect of life that has changed since Petrignani was a junior diplomat in New York and Washington from 1957 through 1968. He told a Columbia University audience in April that 25 years ago Italian Americans' "political power was almost entirely concentrated at a local or state level. Their representatives in Congress did not even number a dozen. They had only one senator, Rhode Island's John Pastore. One generation later, many of them play a prominent political role at a national level."

Petrignani, author of a soon-to-be-published history of Italian foreign policy in the 19th century following the unification of Italy, has given considerable time to observing how far Italian Americans have come in a quarter of a century.

"I remember the Italian Americans at the huge banquets on Columbus Day at the Waldorf Astoria in 1957 and 1958. There was something provincial in those faces. Today, at the same banquets," Petrignani told his audience at Columbia, "the public is incomparably more refined. The Italian Americans no longer have the air of immigrants or foreigners. They have become equal to all other Americans, perhaps even a little more elegant."

The only member of his family who did not become an architect, Petrignani is on the road making speeches at Italian trade shows, awards ceremonies and foreign affairs councils when his Washington schedule is light. His words may vary but never his message.

"Italy has become fashionable," he said at Columbia, "for her industrial and artistic creativity, for the amazing vitality of her economy, for her successful and courageous struggle against terrorism, for her consistent and reliable foreign policy."

He believes that in his four years in Washington, Italian foreign policy has become more assertive and more dynamic, and the result has been that America's movers and shakers are paying more attention to Italy's role in international politics.

Where the credit lies is not that clear, but it is a gratifying time to be the Italian ambassador in Washington. On the other hand, nothing is taken for granted.

"At the end of the day," Petrignani said at the end of one recent day, "I sometimes wonder, 'Have I seen all the people I could see, have I talked to all the people I could talk to, have I discovered all I could discover?' "