A New Notion of Effective Resistance for Directed Graphs-Part II: Computing Resistances

A New Notion of Effective Resistance for Directed Graphs-Part II: Computing Resistances

In Part I of this work we defined a generalization of the concept of effective resistance to directed graphs, and we explored some of the properties of this new definition. Here, we use the theory developed in Part I to compute effective resistances in some prototypical directed graphs. This explora...

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Veröffentlicht in:IEEE transactions on automatic control 2016-07, Vol.61 (7), p.1737-1752
Hauptverfasser: Young, George Forrest, Scardovi, Luca, Leonard, Naomi Ehrich
Format: Artikel
Sprache:eng
Schlagworte:
Automatic control
Computation
directed graphs
effective resistance
Exploration
Gold
Graph theory
Graphs
Joining processes
Laplace equations
Networked control systems
networks
Resistance
Resistors
Symmetric matrices
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Zusammenfassung:In Part I of this work we defined a generalization of the concept of effective resistance to directed graphs, and we explored some of the properties of this new definition. Here, we use the theory developed in Part I to compute effective resistances in some prototypical directed graphs. This exploration highlights cases where our notion of effective resistance for directed graphs behaves analogously to our experience from undirected graphs, as well as cases where it behaves in unexpected ways.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2015.2481839