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Acyclic Graphs

By: Duncan Smith | Edited by: Paul Atkinson, Sara Delamont, Alexandru Cernat, Joseph W. Sakshaug & Richard A. Williams Published: 2020 | Length: 5 | DOI: |
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An acyclic graph is simply a graph that contains no cycles. Graphs are abstract mathematical objects containing vertices (or nodes) and edges (or arcs) between pairs of vertices. Vertices can represent arbitrary entities such as people, variables, or letters of an alphabet. Edges represent binary relations between the vertices they connect. The relation will depend on the application, and it is possible to have distinct relations associated with distinct edges. More often all the graph nodes will correspond to a single entity type and all graph edges will represent the same relation. For asymmetric relations such as a parent–child relation, the edge is directed from the parent to the child. For symmetric relations such as a nonzero partial correlation between variables, the edge will be ...

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