There is something reassuring about seeing all of America’s living presidents together, even if such reunions generally take place only during the most somber of occasions — like the death of one of their own.

However flawed the individuals — and Gerald Ford, Jimmy Carter, George H.W. Bush, Bill Clinton and George W. Bush will always have plenty of detractors — their presence at Ronald Reagan’s funeral Friday was a reminder that Americans indeed live in a democracy, that the power of individual presidents is nothing if not fleeting.

[IMGCAP(1)] And each, in his own way, is a uniquely American success story.

This quintet of presidents is particularly fascinating to contemplate, because each one is linked in some fashion to the others. And not just in the obvious ways.

It was barely mentioned during all the coverage of Reagan’s funeral, but these guys, these ultimate Players (in the spirit of this column), have a history.

Take Ford, the only person ever to serve in the White House without being elected president or vice president. Elevated to the second highest, and then the highest, office in the land in the wake of two scandals, he won the Republican presidential nomination in 1976 by the slimmest of margins over the man everyone has been honoring during the past 10 days.

While Ford and Reagan are celebrated as among the most genial men ever to occupy the Oval Office, theirs was a bitter, protracted, ideologically driven battle that revealed splits in the national GOP that exist to this day.

Ford limped out of the Republican convention to face a little-known ex-governor of Georgia named Jimmy Carter. That campaign was also tough — and made permanent the now-quadrennial tradition of televised presidential debates.

Carter’s victory, the first by a Democratic presidential candidate in a dozen years, was slim. A swing of a few thousand votes in Ohio and Hawaii would have thrown the election to Ford.

In 1980, Reagan was the Republican nominee, beating the elder Bush and others for the Republican nod. (One of those he beat, former Texas Gov. John Connally, had close ties to two other ex-presidents: Lyndon Johnson and Richard Nixon). After flirting with the idea of naming Ford as his running mate, Reagan instead opted for Bush, who had served as CIA director under Ford. They went on to a landslide victory over Carter, who was weakened by high inflation and unemployment rates as well as the 444-day hostage crisis in Iran.

Largely forgotten in Reagan’s obituaries was the fact that he did not make his first run for the White House in 1976. A man of unbridled ambition beneath his sunny veneer, he briefly sought the Republican presidential nomination in 1968 against Richard Nixon and Nelson Rockefeller after serving less than two years as governor of California.

Nixon, of course, was elected and re-elected, and made Ford his vice president after Spiro Agnew resigned in 1973. Ford, ascending to the presidency in 1974 after Nixon’s resignation, made Rockefeller his vice president but then shunted Rockefeller aside in the 1976 election as a nod to the Reagan wing’s growing power in the GOP.

Cast out of office in their re-election bids, Ford and Carter became close friends in the early 1980s and have joined together for a variety of good works in the ensuing years.

Reagan and Bush, meanwhile, steamrolled to an even bigger landslide in 1984 against Carter’s vice president, Walter Mondale.

In 1988, after waiting patiently for eight years, George H.W. Bush won the Republican nomination, defeating, among others, Senate Republican Leader Bob Dole (Kan.), who had been Ford’s running mate in 1976 (and who, by most accounts, had been outclassed by Mondale in their debate that year).

The Democrats in 1988 nominated Massachusetts Gov. Michael Dukakis, who had no obvious connections to other presidents or presidential contenders, but who was compared to Carter in at least one Republican TV ad anyway. Bush won what many pundits referred to as Reagan’s “third term.”

Four years later, though, Bush was booted from office by Arkansas Gov. Bill Clinton — 16 years after the previous Democratic White House victory.

Twelve years earlier, Clinton had been bounced from office by Arkansas voters after a mere two years as governor. Back then he was considered a victim, to at least some degree, of Carter’s policy allowing Cuban refugees into the United States in 1979 and 1980. (The refugees, rightly or wrongly, were blamed for a crime wave in the cities where they wound up.)

Clinton served two terms with Al Gore as his vice president — defeating Dole in their re-election bid in 1996.

In 2000, it was Gore’s turn to seek his own White House term, but he was defeated by George W. Bush — aided, Democratic cynics have said, by Supreme Court justices appointed by Reagan and the first President Bush.

All of which goes to show that the world of politics at that rarefied level is very small indeed.