David Burstein

​Swarthmore College
Department of Mathematics and Statistics
Visiting Assistant Professor
Research expertise in network science, graph theory,
data science, stochastic processes and dynamical systems.
Interception in distance vector routing networks

To address security issues in routing networks, we analyze how routers can appear trustworthy and lie about their position in the network to intercept traffic.

Figure: A​ real-life incident in connection with traffic interception.  

The target is the British Telecom, which services the UK Atomic Weapons Establishment.  

A typical path from the node in Texas to the British Telecom is illustrated in blue, while the path taken when the traffic was intercepted is highlighted in red.


Asymptotic e​​​​​​​numeration of graphs with prescribed degree sequences 

We develop a novel method that yields arbitrarily accurate approximations for the number of graphs that realize a prescribed degree sequence under a flexible sparsity constraint.  

Counting the number of graphs with a prescribed degree sequence arises in a number of diverse applications.  

In community detection, a form of unsupervised learning, we try to identify a hidden community in a network based on the assumption that nodes in the same community are more likely to share an edge.  We can identify these communities by enumerating the number of graphs that realize the same prescribed degree sequence with similar community structure to find statistical anomalies.

For random network generation, while there are many methods for constructing a network with a prescribed degree sequence, we often want to generate each distinct network that realizes the given degree sequence with equal probability.  Deriving the aforementioned enumeration results informs us on how to wire up a network without introducing bias. 
FigureIn the community detection problem, we need to identify hidden communities in the network. For this example, each community is marked with a different color.