WASHINGTON -- A new book by The Washington Post's Bob Woodward describes U.S. Sen. Lindsey Graham as playing a central role in the formation and execution of President Barack Obama's war policy in Afghanistan through his close ties to Vice President Joe Biden, Gen. David Petraeus and White House Chief of Staff Rahm Emanuel.

The book by the former Watergate reporter, "Obama's Wars," contains vivid and previously undisclosed portrayals of Graham's closed-door conversations and confrontations with Obama, Afghan President Hamid Karzai and other key figures.

Petraeus, the former commander of U.S. troops in Iraq who now holds the same post in Afghanistan, describes Graham as "a brilliant and skillful chess player" whom the general admires for his ability to navigate the power channels of Washington.

Graham, a South Carolina Republican, returned the praise Tuesday, predicting that Petraeus will go down in history as one of the greatest American generals.

"I'm just flattered (by Petraeus' praise) because I have such respect for him," Graham said. "He is probably the most well-rounded person I have ever met. General Petraeus has a depth of knowledge about military geopolitical matters that's astounding, as far as I'm concerned."

Graham confirmed the book's portrayal of him and Petraeus as having frequent, ongoing contact, with the general providing detailed updates on U.S. military progress and setbacks in Iraq and now Afghanistan, and the senator advising him on political realities.

Graham said he and Petraeus once discussed whether the general would consider a political career.

"He made a joke out of it," Graham recalled Tuesday.

"He said he would just stick with being shot at; combat was maybe a better deal than doing what I was doing (as a senator)."