Related papers: Empirical Sampling of Connected Graph Partitions f…
Most methods proposed to uncover communities in complex networks rely on combinatorial graph properties. Usually an edge-counting quality function, such as modularity, is optimized over all partitions of the graph compared against a null…
In this work, Transition Probability Matrix (TPM) is proposed as a new method for extracting the features of nodes in the graph. The proposed method uses random walks to capture the connectivity structure of a node's close neighborhood. The…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
An important problem arising in the study of complex networks, for instance in community detection and motif finding, is the sampling of graphs with fixed degree sequence. The equivalent problem of generating random 0,1 matrices with fixed…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
We examine the mixing time for random walks on graphs. In particular we are interested on investigating graphs with bottlenecks. Furthermore, the cutoff phenomenon is examined.
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…
Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically.…
We propose three novel gerrymandering algorithms which incorporate the spatial distribution of voters with the aim of constructing gerrymandered, equal-population, connected districts. Moreover, we develop lattice models of voter…
The statistics of first-passage times of random walks to target sites has proved to play a key role in determining the kinetics of space exploration in various contexts. In parallel, the number of distinct sites visited by a random walker…
In this paper, we provide faster algorithms for computing various fundamental quantities associated with random walks on a directed graph, including the stationary distribution, personalized PageRank vectors, hitting times, and escape…
We consider the problem of uniformly generating a spanning tree, of a connected undirected graph. This process is useful to compute statistics, namely for phylogenetic trees. We describe a Markov chain for producing these trees. For cycle…
The task of \emph{community detection} in a graph formalizes the intuitive task of grouping together subsets of vertices such that vertices within clusters are connected tighter than those in disparate clusters. This paper approaches…
The recent wave of attention to partisan gerrymandering has come with a push to refine or replace the laws that govern political redistricting around the country. A common element in several states' reform efforts has been the inclusion of…
We study the mixing time of random graphs in the $d$-dimensional toric unit cube $[0,1]^d$ generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a…
We consider a discrete-time Markovian random walk with resets on a connected undirected network. The resets, in which the walker is relocated to randomly chosen nodes, are governed by an independent discrete-time renewal process. Some nodes…
Since 1997 a considerable effort has been spent to study the mixing time of switch Markov chains on the realizations of graphic degree sequences of simple graphs. Several results were proved on rapidly mixing Markov chains on unconstrained,…
Many regular graphs admit a natural partition of their edge set into cliques of the same order such that each vertex is contained in the same number of cliques. In this paper, we study the mixing rate of certain random walks on such graphs…
The complexity of biological, social and engineering networks makes it desirable to find natural partitions into communities that can act as simplified descriptions and provide insight into the structure and function of the overall system.…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…