In the following paper , the authors proposed a new method to compute the most important edges (or links) in a network:

*Grady, D., Thiemann, C., & Brockmann, D. (2012). Robust classification of salient links in complex networks. Nature Communications, 3(May), 864:1–864:10. doi:10.1038/ncomms1847*

This method automatically finds “salient” links in networks by using the following approach:

- Choose a property that defines the weight of an edge in a given network,
- Define the distance between two nodes as 1 / the weight,
- Using above distance measure, take a node and compute the shortest path to all other nodes in the network,
- Combine all edges from the previous step into a set, which is called the Shortest Path Tree (SPT),
- For each edge in the SPT, increase a “salience” counter,
- Repeat steps 3-5 for every other node in the network,
- For each edge, divide its salience counter by the total number of nodes in the network, leading to a salience property with a value in the range [0..1].

You can find an interesting application example in:

*Jonatan Samoocha. Finding Important Connections In A Network – Automatically. http://blog.xebia.com/2013/01/21/finding-important-connections-in-a-network-automatically/*

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