David Burstein

email: dburste1*at*swarthmore*dot*edu
Visiting Assistant Professor at Swarthmore College
Research Interests:  ​Network Science, Dynamical Systems and Stochastic Processes. 
Applications to Internet Routing, Epidemiology and Neuroscience.
Generating Random Networks to Understand the Impact of Network Structure on Dynamics

In order to ascertain the impact of the network architecture on the underlying dynamics (in an epidemiological, 
genetic or biological neural network), we would like an ensemble of tools for generating networks that emulate 
many of the properties of their real-world counterparts. More specifically, a considerable amount of research 
has demonstrated the importance of the degree sequence, a list of the number of edges for each node, in 
influencing the dynamical behavior of the network. To address this problem of generating synthetic networks 

of interest, in our paper  Sufficient conditions for graphicality of bidegree sequences  we provide flexible 
and easy-to-use sufficient conditions to verify that a given degree sequence does correspond to an actual network.  

Furthermore in 
Degree switching and partitioning for enumerating graphs to arbitrary orders of accuracy
we explore how to asymptotically count the number of networks that correspond to a 'sparse' degree sequence.
Exploiting Properties of Real World Networks to Construct Computationally Efficient Solutions

Calculating almost shortest paths between two nodes arises in many applications. Such applications include, 
inferring the spreading path of a pathogen in a social network, exploring complex relationships between 
biological entities, identifying membership of hidden communities in a graph and routing in the autonomous 
system (AS) graph. We stress that since we want to find many almost shortest paths in these real world

networks, we would like a computationally efficient method for finding these almost shortest paths.

In our work, The k shortest paths problem with application to routing , we exploit properties of real world networks, in particular small average path length, to construct an efficient solution for quickly finding almost shortest paths.