(definition)

**Definition:**
A *connected graph* where "layers" L_{0} ... L_{k} *partition* the *vertices*. Each *edge*, which has a nonnegative integral *weight*, connects only vertices in successive layers. The width is the greatest number of vertices in any layer, i.e., MAX_{i=0}^{k} |L_{i}|.

**Generalization** (I am a kind of ...)

*connected graph*.

**Specialization** (... is a kind of me.)

*bipartite graph*.

*Note:
A bipartite graph is a layered graph with two layers. *

* A. Fiat, D.P. Foster, H.J. Karloff, Y. Rabani, Y. Ravid, and S. Vishwanathan. Competitive Algorithms for Layered Graph Traversal. SIAM J. Comput., to appear. Preliminary version appeared in FOCS '91. Contributed by Giovanni Fiaschi <Giovanni.Fiaschi@marconi.com> June 2000.*

Author: PEB

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Entry modified 11 April 2005.

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Cite this as:

Paul E. Black, "layered graph", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 11 April 2005. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/layeredgraph.html