Related papers: Complexity and Geometry of Sampling Connected Grap…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…
We study the problem of approximately counting the number of list packings of a graph. The analogous problem for usual vertex coloring and list coloring has attracted a lot of attention. For list packing the setup is similar but we seek a…
Random walk sampling methods have been widely used in graph sampling in recent years, while it has bias towards higher degree nodes in the sample. To overcome this deficiency, classical methods such as MHRW design weighted walking by…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
We study the computational complexity of the map redistricting problem (gerrymandering). Mathematically, the electoral district designer (gerrymanderer) attempts to partition a weighted graph into $k$ connected components (districts) such…
Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges…
Small-world graphs, which combine randomized and structured elements, are seen as prevalent in nature. Jon Kleinberg showed that in some graphs of this type it is possible to route, or navigate, between vertices in few steps even with very…
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…
Many online networks are measured and studied via sampling techniques, which typically collect a relatively small fraction of nodes and their associated edges. Past work in this area has primarily focused on obtaining a representative…
This paper presents the results of an experimental study of graph partitioning. We describe a new heuristic technique, path optimization, and its application to two variations of graph partitioning: the max_cut problem and the…
We propose SWING: Space Walks for Implicit Network Graphs, a new class of algorithms for computations involving Graph Random Features on graphs given by implicit representations (i-graphs), where edge-weights are defined as bi-variate…
We present an elementary way to transform an expander graph into a simplicial complex where all high order random walks have a constant spectral gap, i.e., they converge rapidly to the stationary distribution. As an upshot, we obtain new…
In network modeling of complex systems one is often required to sample random realizations of networks that obey a given set of constraints, usually in form of graph measures. A much studied class of problems targets uniform sampling of…
Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the…
We compare discrete-time quantum walks on graphs to their natural classical equivalents, which we argue are lifted Markov chains, that is, classical Markov chains with added memory. We show that these can simulate quantum walks, allowing us…
In the United States, regions are frequently divided into districts for the purpose of electing representatives. How the districts are drawn can affect who's elected, and drawing districts to give an advantage to a certain group is known as…
It has been shown recently that graph signals with small total variation can be accurately recovered from only few samples if the sampling set satisfies a certain condition, referred to as the network nullspace property. Based on this…
We present a novel quasi-Monte Carlo mechanism to improve graph-based sampling, coined repelling random walks. By inducing correlations between the trajectories of an interacting ensemble such that their marginal transition probabilities…
We introduce Tiered Sampling, a novel technique for approximate counting sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size $M$, which…