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The Internet has become a critical component of modern civilization requiring scientific exploration akin to endeavors to understand the land, sea, air, and space environments. Understanding the baseline statistical distributions of traffic are essential to the scientific understanding of the Internet. Correlating data from different Internet observatories and outposts can be a useful tool for gaining insights into these distributions. This work compares observed sources from the largest Internet telescope (the CAIDA darknet telescope) with those from a commercial outpost (the GreyNoise honeyfarm). Neither of these locations actively emit Internet traffic and provide distinct observations of unsolicited Internet traffic (primarily botnets and scanners). Newly developed GraphBLAS hyperspace matrices and D4M associative array technologies enable the efficient analysis of these data on significant scales. The CAIDA sources are well approximated by a Zipf-Mandelbrot distribution. Over a 6-month period 70% of the brightest (highest frequency) sources in the CAIDA telescope are consistently detected by coeval observations in the GreyNoise honeyfarm. This overlap drops as the sources dim (reduce frequency) and as the time difference between the observations grows. The probability of seeing a CAIDA source is proportional to the logarithm of the brightness. The temporal correlations are well described by a modified Cauchy distribution. These observations are consistent with a correlated high frequency beam of sources that drifts on a time scale of a month. 

The Internet has never been more important to our society, and understanding the behavior of the Internet is essential. The Center for Applied Internet Data Analysis (CAIDA) Telescope observes a continuous stream of packets from an unsolicited darkspace representing 1/256 of the Internet. During 2019 and 2020 over 40,000,000,000,000 unique packets were collected representing the largest ever assembled public corpus of Internet traffic. Using the combined resources of the Supercomputing Centers at UC San Diego, Lawrence Berkeley National Laboratory, and MIT, the spatial temporal structure of anonymized source-destination pairs from the CAIDA Telescope data has been analyzed with GraphBLAS hierarchical hyper-sparse matrices. These analyses provide unique insight on this unsolicited Internet darkspace traffic with the discovery of many previously unseen scaling relations. The data show a significant sustained increase in unsolicited traffic corresponding to the start of the COVID19 pandemic, but relatively little change in the underlying scaling relations associated with unique sources, source fan-outs, unique links, destination fan-ins, and unique destinations. This work provides a demonstration of the practical feasibility and benefit of the safe collection and analysis of significant quantities of anonymized Internet traffic. 

The Internet is transforming our society, necessitating a quantitative understanding of Internet traffic. Our team collects and curates the largest publicly available Internet traffic data containing 50 billion packets. Utilizing a novel hypersparse neural network analysis of “video” streams of this traffic using 10,000 processors in the MIT SuperCloud reveals a new phenomena: the importance of otherwise unseen leaf nodes and isolated links in Internet traffic. Our neural network approach further shows that a two-parameter modified Zipf-Mandelbrot distribution accurately describes a wide variety of source/destination statistics on moving sample windows ranging from 100,000 to 100,000,000 packets over collections that span years and continents. The inferred model parameters distinguish different network streams and the model leaf parameter strongly correlates with the fraction of the traffic in different underlying network topologies. The hypersparse neural network pipeline is highly adaptable and different network statistics and training models can be incorporated with simple changes to the image filter functions. 

The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix-based graph algorithms to the broadest possible audience. Mathematically, the GraphBLAS defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, the two are easily connected by matrix multiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of a small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.