Rankings in Dark Social Networks


  • Geoffrey Wang*

  • Max Zhao*

  • Others (see text)

While at Davidson College I worked with students Max Zhao and Geoffrey Wang on detecting ‘shadow players’ in complex networks. In other words, we worked to identify influential players in social networks who may otherwise want to remain undetected, such as influencers in terrorist cell networks or dark net markets. Our idea was to take the usual centrality rankings and ‘wiggle’ them continuously by a random walk to reduce the rank of those who are central and thereby relatively increase the ranking of those who are less central. We applied this to the terrorist cell from the 9/11 attack as our main example, the analysis of which is promising as it agrees with our hindsight understanding of that cell’s structure. The students were essential in coming up countless extremal examples for various scenarios and crafting code to compare dozens of possible ranking methods. Extensions of this project are certainly accessible to student involvement.

Details and coauthors purposefully omitted, I also have a few projects concerning other dark social networks.

A social network consisting on the 9/11 terrorists.

The original 9/11 social network, constructed by Valdis Krebs in Mapping Networks of Terrorist Cells.

Four copies on the 9/11 social network, labeled Pagerank, Degree, Closeness, and Betweenness. Sizes of nodes vary in the pictures based on their relative ranking in these measures.

Some traditional ranking methods applied to the 9/11 social network: Pagerank, degree, closeness, and betweenness. This yields useful information on the "most important" players, such as Mohamed Atta (the ring leader), but secondary players are hard to identify. This is primarily because the unusual structure of social networks wherein players attempt to stay anonymous.

The 9/11 terrorist network, with nodes of various sizes (depending on their relative ranking).

Our ranking method highlights secondary players. In conjuction with the usual rankings above, this gives a more complete picture on the structure of the network.


I am quite interested in rankings of networks in general, whether those are social networks, dark social networks, or any other flavor. Students with interest in graph theory and its applications should feel free to contact me to talk about potential projects! Background in linear algebra is all that's needed. Some coding background would be helpful but not required.