Related papers: The Balanced Up-Down Walk

We introduce an algorithm for generating a random sequence of fragmentation trees, which we call the ancestral branching algorithm. This algorithm builds on the recursive partitioning structure of a tree and gives rise to an associated…

Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…

Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs.…

Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…

In this paper, we study the graph-based semi-supervised learning for classifying nodes in attributed networks, where the nodes and edges possess content information. Recent approaches like graph convolution networks and attention mechanisms…

This work considers the general task of estimating the sum of a bounded function over the edges of a graph, given neighborhood query access and where access to the entire network is prohibitively expensive. To estimate this sum, prior work…

The shortest-path, commute time, and diffusion distances on undirected graphs have been widely employed in applications such as dimensionality reduction, link prediction, and trip planning. Increasingly, there is interest in using…

We introduce weighted Markovian graphs, a random walk model that decouples the transition dynamics of a Markov chain from (random) edge weights representing the cost of traversing each edge. This decoupling allows us to study the…

Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified tensor framework for modeling higher-order Markov chains…

The symmetric random walk is known to be recurrent in one and two dimensions, and becomes transient in three or higher dimensions. We compare the symmetric random walk to walks driven by certain \polya\ urns. We show that, in contrast, if…

We introduce and develop the concept of Maximal Entropy Random Walks (MERWs) on Weighted Bratteli Diagrams (WBDs), maximizing entropy production along paths as a natural criterion for choosing random walks on networks. Initially defined for…

Predicting the occurrence of links is a fundamental problem in networks. In the link prediction problem we are given a snapshot of a network and would like to infer which interactions among existing members are likely to occur in the near…

This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…

We introduce a new graph polynomial that encodes interesting properties of graphs, for example, the number of matchings and the number of perfect matchings. Most importantly, for bipartite graphs the polynomial encodes the number of…

This article introduces a novel communication scheme, termed coded compressed sensing, for unsourced multiple-access communication. The proposed divide-and-conquer approach leverages recent advances in compressed sensing and forward error…

Finding the reduced-dimensional structure is critical to understanding complex networks. Existing approaches such as spectral clustering are applicable only when the full network is explicitly observed. In this paper, we focus on the online…

We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…

This paper proposes a new type of recurrence where we divide the Markov chains into intervals that start when the chain enters into a subset A, then sample another subset B far away from A and end when the chain again return to A. The…

We address the problem of building and maintaining distributed spanning trees in highly dynamic networks, in which topological events can occur at any time and any rate, and no stable periods can be assumed. In these harsh environments, we…

We consider transport over a strongly connected, directed graph. The scheduling amounts to selecting transition probabilities for a discrete-time Markov evolution which is designed to be consistent with certain initial and final marginals.…