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:20 July 2016

A lot of datasets these days come in the form of large and complex networks. They describe intricate systems with entities being modeled as nodes and their relationships as edges. These networks contain a wealth of information, but that information is often hidden within network patterns which are difficult to uncover. While deciphering these patterns is crucial, computational analyses of large networks are often intractable. So, many questions we ask about the world cannot be answered exactly even with unlimited compute power and time. Our only hope is to answer these questions approximately (i.e., heuristically) and prove how far the approximate answer is from the exact one in the worst case. So far, a majority of scalable heuristics for network analysis consider only simple descriptors of a network such as node count and degree, capturing only its lower-order connectivity patterns. But they suffer from a severe limitation: two networks can appear similar when viewed through the lens of simple descriptors, but can reveal a very different connectivity structure when we change the lens to include higher-order descriptors called graphlets (small subgraphs). While this limitation has been known for some time, nothing could be done because this was a tough nut to crack. A scalable technique for uncovering higher-order organization of large networks - at the level of graphlets - was not on the horizon. But to my surprise, I came across a recent article by Benson et al. titled "Higher-order organization of complex networks" in Science (2016) where they propose a new framework for clustering networks on the basis of higher-order connectivity patterns, with guarantees on the optimality of obtained clusters and which scales to billions of edges. This is such an amazing result. Kudos to Benson at al.
  • Benson, A. R., Gleich, D. F., & Leskovec, J. (2016). Higher-order organization of complex networks. Science, 353(6295), 163-166.

Last modified 20 July 2016 at 4:27 pm by svattam