Leader election algorithm in a directed graph

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I'm trying to find a leader election algorithm given a directed graph. What I've found till now is that most LE algorithms have a ring network or a mesh topology. Can anyone suggest me some algorithms?

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"An introduction to Distributed Algorithms" by Tel covers this in chapter 7. Here are some mentions that might be search terms "tree algorithm" - fairly straightforward algorithm to find the min on a tree. Finn's algorithm is a reference to a Wave algorithm from a previous chapter which would be relatively inefficient if used for leader election. Tel says the leader election problem on arbitrary networks is closely related to spanning tree creation and describes Gallager-Humblet-Spira. Korach-Kutten-Moran apparently describe how to turn a traversal algorithm for general networks into a leader election algorithm.