, Volume 81, Issue 4, pp 1535–1560 | Cite as

A Polynomial-Time Algorithm for Detecting the Possibility of Braess Paradox in Directed Graphs

  • Pietro Cenciarelli
  • Daniele GorlaEmail author
  • Ivano Salvo


A directed multigraph is said vulnerable if it can generate Braess paradox in traffic networks. In this paper, we give a graph–theoretic characterisation of vulnerable directed multigraphs. Analogous results appeared in the literature only for undirected multigraphs and for a specific family of directed multigraphs. The proof of our characterisation provides the first polynomial time algorithm that checks if a general directed multigraph is vulnerable in \(\mathcal{O}(|V| \cdot |E|^2)\). Our algorithm also contributes to the directed subgraph homeomorphism problem without node mapping, by providing another pattern graph for which a polynomial time algorithm exists.


Braess paradox Traffic networks Graph theory Graph algorithms Subgraph homeomorphism 



We are very grateful to the anonymous referees, whose careful reading has radically improved a preliminary version of this work.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceSapienza University of RomeRomeItaly

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