Revivalist preacher Billy Graham begins a week-long visit here tonight, that carries with it the seeds of another revival - a quiet but steady improvement in relations with the U.S. being sought by Hungarian Communist leader Janos Kadar.

That is the view of a number of U.S. specialists on East Europe who are watching with great interest what is - with the exception of a 1967 trip to nonaligned Yugoslavia - the first visit of Graham to a Communist country in some three decades of preaching around the world.

The invitation to the Baptist preacher came from the president of the Council of Free Churches in Hungary, Sandor Palotay. But the fact that it was approved by the Kadar government "is definitely a signal to the U.S. that they want better relations. It was also very clever. They are smart enough to know that Jimmy Carter is a Baptist, says one Western official.

On his arrival in Budapest today, Graham said he would deliver a "very general message" from President Carter to Hungarian church leaders and their congregations. He said he was not carrying any political message from the White House.

Actually, specialist see the Graham invitation as part of a pattern that suggest the Kadar government is seeking a more relaxed approach in its foreign policy. Hungary feels it has earned some flexibility from the Kremlin in handling its internal affairs during the 21 years of Kadar's rule.

On the surface, the visit of such an exciting and skillful orator as Graham to a country that is still tightly controlled would appear to be risky for the government here.

But Western specialists tend to feel the risk is low. For one thing, Graham will be speaking in English, and translations will no dount lose some of the steam that makes him so effective. In recent years, the common Western view of the 64-years-old Kadar, who has held office longer than any leader in the Soviet-led Warsaw pact, has been that his strict adherence to Soviet foreign policy earned him the trust of the Kremlin. This allowed him greater leeway at home, something which has helped make Hungary the least repressive country of any within the Soviet bloc.

That view till holds, specialists say. But they now also detest more efforts by Kadar, perhaps sensing the end of the Brezhnev era in the Soviet Union and perhaps the end of his own rule, to gain more foreign policy freedom as well adn to "build up credit and respect in the West, especially where it counts - in the U.S. and West Germany," says one experienced observer.

Aside from the Graham visit, sources cite the cautions but important recent efforts by the Budapest government to improve relations with Hungary's Roman Catholic church and the Vatican, an area that has been a lingering source of hard feelings in U.S.-Hungarian relations dating back to the days when the late Jozsef Cardinal Mindszenty was forced into exile.

The cordiality with which visiting U.S. Senator George McGovern was received here last month also fits that pattern, especially when McGovern sided with those who feel the U.S. ought to return the crown jewels of St. Stephen, Hungary's patron saint. Those jewels fell into U.S. hands at the end of World War II and the U.S. position that they will be returned when there is "a general improvement" in relations is a continuing source of bitterness in a country where roughly two-thirds of its 11 million people are Catholic.

Kadar also let it be known recently that he does not agree with the Kremlin's hard line against the more liberal brand of Eurocommunism now evident in Western Communist parties.This position appears to have annoyed the Soviets, who have apparently rebuked Kadar for it, but his views became known nevertheless.

The Hungarian Communist chief also recently begun to visit the West, especially his country's important trading partner. With the exception of a trip to Helsinki in 1975 has never done this before. Yet, in December he went to neutral Austria and in June to Italy and last month to West Germany, both members of the North Atlantic Alliance.

Though much of Billy Graham's career and oratory was based on a staunch anti-communis, his denunciations of atheistic communism has been more restained in recent years. The southern Baptist minister, nearing his 59th birthday, has suggested that he wants to devote his later years to preaching to as many people as he can in socialist and non-socialist countries and that to do that he may have to leave political questions behind.

Before Graham's arrival, Palotay told reporters that while Graham had some "misconceptions" about the East, his "integrity and sincere conviction stand beyond doubt" and his goodwill mission to Hungary will be "a projection of the Helsinki spirit to the religious field" This reference to the Helsinki agreements on European security also reflects the clear foreign policy overtones of the Graham trip.

In the Soviet Union, the Baptists are one of the more outspoken minority groups, something which earns them an extra measure of Kremlin repression. Thurs, Kadar's willingness to allow the world's most well-known Baptist preacher into his Communist domain also reflects his attempt at broader international policy. It also probably reflects, specialists believe, the fact the Soviets too, are capable of some flexibility.

Graham will give a series of lectures and sermons and officiate at church services - and "will not be restricted in any way," Palotay told reporters. But the Hungarian church man also said the visit will not be 'crusade-orieneted."