Related papers: Census Dual Graphs: Properties and Random Graph Mo…

In representative democracy, a redistricting map is chosen to partition an electorate into districts which each elects a representative. A valid redistricting map must satisfy a collection of constraints such as being compact, contiguous,…

Statistical pattern classification methods based on data-random graphs were introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the data points from various classes.…

Redistricting is the problem of partitioning a set of geographical units into a fixed number of districts, subject to a list of often-vague rules and priorities. In recent years, the use of randomized methods to sample from the vast space…

Gerrymandering is one of the biggest threats to American democracy. By manipulating district lines, politicians effectively choose their voters rather than the other way around. Current gerrymandering identification methods (namely the…

Clustering a graph, i.e., assigning its nodes to groups, is an important operation whose best known application is the discovery of communities in social networks. Graph clustering and community detection have traditionally focused on…

Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly-planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations.…

Partisan gerrymandering poses a threat to democracy. Moreover, the complexity of the districting task may exceed human capacities. One potential solution is using computational models to automate the districting process by optimizing…

Fine resolution estimates of demographic and socioeconomic attributes are crucial for planning and policy development. While several efforts have been made to produce fine-scale gridded population estimates, socioeconomic features are…

This paper is to obtain a simple dividing-diagram of the congressional districts, where the only limit is that each district should contain the same population if possibly. In order to solve this problem, we introduce three different…

Choices made by individuals have widespread impacts--for instance, people choose between political candidates to vote for, between social media posts to share, and between brands to purchase--moreover, data on these choices are increasingly…

Graph datasets are frequently constructed by a projection of a bipartite graph, where two nodes are connected in the projection if they share a common neighbor in the bipartite graph; for example, a coauthorship graph is a projection of an…

As a case study into an algorithmic approach to congressional districting, North Carolina provides a lot to explore. Statistical modeling has called into question whether recent North Carolina district plans are unbiased. In particular, the…

Random key graphs were introduced to study various properties of the Eschenauer-Gligor key predistribution scheme for wireless sensor networks (WSNs). Recently this class of random graphs has received much attention in contexts as diverse…

Deep graph clustering (DGC), which aims to unsupervisedly separate the nodes in an attribute graph into different clusters, has seen substantial potential in various industrial scenarios like community detection and recommendation. However,…

Graphs are used to model interactions in a variety of contexts, and there is a growing need to quickly assess the structure of such graphs. Some of the most useful graph metrics are based on triangles, such as those measuring social…

This paper presents a graph bundling algorithm that agglomerates edges taking into account both spatial proximity as well as user-defined criteria in order to reveal patterns that were not perceivable with previous bundling techniques. Each…

We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…

We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. http://www.ams.org/mathscinet-getitem?mr=MR2123250) and for the self-duality of Feller's branching…

The application of the network approach to the urban case poses several questions in terms of how to deal with metric distances, what kind of graph representation to use, what kind of measures to investigate, how to deepen the correlation…

Deciding whether a political districting plan was distorted by a hidden agenda, or whether it dilutes the voting power of some group, requires a neutral baseline for comparison. Remarkably, all nine U.S. Supreme Court justices have now…