Graphs and paradoxes

A directed graph is a pair where N is any collection or set of objects (the nodes of the graph) and E is a relation on N (the edges). Intuitively speaking, we can think of a directed graph in terms
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A directed graph is a pair <N, E> where N is any collection or set of objects (the nodes of the graph) and E is a relation on N (the edges). Intuitively speaking, we can think of a directed graph in terms of a dot-and-arrow diagram, where the nodes are represented as dots, and the edges are represented as arrows. For example, in the following figure we have a graph that consists of three nodes–A, B, and C, and four edges: one from A to A, one from A to B, one from B to C, and one from C to B. Image courtesy of author. Note that with directed graphs we distinguish between those cases where a node has an arrow from itself to itself and those cases where it does not, and we also take into account the direction of the edge–that is, the edge from B to C is distinct from the edge from C to B (we do, however, represent cases where we have arrows going in both directions with a single line with two “arrowheads”). In the diagram above, the nodes might represent Alice, Betty,. . .

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News source: OUPblog » Philosophy

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