
A Polynomial Kernel for Line Graph Deletion
The line graph of a graph G is the graph L(G) whose vertex set is the ed...
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On spectral embedding performance and elucidating network structure in stochastic block model graphs
Statistical inference on graphs often proceeds via spectral methods invo...
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The Four Point Permutation Test for Latent Block Structure in Incidence Matrices
Transactional data may be represented as a bipartite graph G:=(L ∪ R, E)...
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Nonsingular (VertexWeighted) Block Graphs
A graph G is nonsingular (singular) if its adjacency matrix A(G) is nons...
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Statistical inference on errorfully observed graphs
Statistical inference on graphs is a burgeoning field in the applied and...
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Universally Consistent Latent Position Estimation and Vertex Classification for Random Dot Product Graphs
In this work we show that, using the eigendecomposition of the adjacenc...
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On identifying unobserved heterogeneity in stochastic blockmodel graphs with vertex covariates
Both observed and unobserved vertex heterogeneity can influence block st...
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Beyond the adjacency matrix: random line graphs and inference for networks with edge attributes
Any modern network inference paradigm must incorporate multiple aspects of network structure, including information that is often encoded both in vertices and in edges. Methodology for handling vertex attributes has been developed for a number of network models, but comparable techniques for edgerelated attributes remain largely unavailable. We address this gap in the literature by extending the latent position random graph model to the line graph of a random graph, which is formed by creating a vertex for each edge in the original random graph, and connecting each pair of edges incident to a common vertex in the original graph. We prove concentration inequalities for the spectrum of a line graph, and then establish that although naive spectral decompositions can fail to extract necessary signal for edge clustering, there exist signalpreserving singular subspaces of the line graph that can be recovered through a carefullychosen projection. Moreover, we can consistently estimate edge latent positions in a random line graph, even though such graphs are of a random size, typically have high rank, and possess no spectral gap. Our results also demonstrate that the line graph of a stochastic block model exhibits underlying block structure, and we synthesize and test our methods in simulations for cluster recovery and edge covariate inference in stochastic block model graphs.
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