Flag Complex
In an abstract simplicial complex, a set S of vertices that is not itself part of the complex, but such that each pair of vertices in S belongs to some simplex in the complex, is called an empty simplex. Mikhail Gromov defined the no-Δ condition to be the condition that a complex have no empty simplices. A flag complex is an abstract simplicial complex that has no empty simplices; that is, it is a complex satisfying Gromov's no-Δ condition. Any flag complex is the clique complex of its 1-skeleton. Thus, flag complexes and clique complexes are essentially the same thing. However, in many cases it may be convenient to define a flag complex directly from some data other than a graph, rather than indirectly as the clique complex of a graph derived from that data.
Read more about this topic: Clique Complex
Famous quotes containing the words flag and/or complex:
“Our flag is red, white and blue, but our nation is a rainbow—red, yellow, brown, black and white—and we’re all precious in God’s sight.”
—Jesse Jackson (b. 1941)
“I have met charming people, lots who would be charming if they hadn’t got a complex about the British and everyone has pleasant and cheerful manners and I like most of the American voices. On the other hand I don’t believe they have any God and their hats are frightful. On balance I prefer the Arabs.”
—Freya Stark (1893–1993)