
Counting Motifs with Graph Sampling
Applied researchers often construct a network from a random sample of no...
02/21/2018 ∙ by Jason M. Klusowski, et al. ∙ 0 ∙ shareread it

Estimating the Number of Connected Components in a Graph via Subgraph Sampling
Learning properties of large graphs from samples has been an important p...
01/12/2018 ∙ by Jason M. Klusowski, et al. ∙ 0 ∙ shareread it

Tight Bounds on the Asymptotic Descriptive Complexity of Subgraph Isomorphism
Let v(F) denote the number of vertices in a fixed connected pattern grap...
02/06/2018 ∙ by Oleg Verbitsky, et al. ∙ 0 ∙ shareread it

Dominator Colorings of Digraphs
This paper serves as the first extension of the topic of dominator color...
02/19/2019 ∙ by Michael Cary, et al. ∙ 0 ∙ shareread it

Reducing CMSO Model Checking to Highly Connected Graphs
Given a Counting Monadic Second Order (CMSO) sentence ψ, the CMSO[ψ] pro...
02/05/2018 ∙ by Daniel Lokshtanov, et al. ∙ 0 ∙ shareread it

BiasVariance Tradeoff of Graph Laplacian Regularizer
This paper presents a biasvariance tradeoff of graph Laplacian regulari...
06/02/2017 ∙ by PinYu Chen, et al. ∙ 0 ∙ shareread it

Partitioning into Expanders
Let G=(V,E) be an undirected graph, lambda_k be the kth smallest eigenv...
09/12/2013 ∙ by Shayan Oveis Gharan, et al. ∙ 0 ∙ shareread it
Number of Connected Components in a Graph: Estimation via Counting Patterns
Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that have been surveyed. Inferring a global property of the original graph from such a sampled subgraph is of a fundamental interest. In this work, we focus on estimating the number of connected components. It is a challenging problem and, for general graphs, little is known about the connection between the observed subgraph and the number of connected components of the original graph. In order to make this connection, we propose a highly redundant and largedimensional representation of the subgraph, which at first glance seems counterintuitive. A subgraph is represented by the counts of patterns, known as network motifs. This representation is crucial in introducing a novel estimator for the number of connected components for general graphs, under the knowledge of the spectral gap of the original graph. The connection is made precise via the Schatten knorms of the graph Laplacian and the spectral representation of the number of connected components. We provide a guarantee on the resulting mean squared error that characterizes the bias variance tradeoff. Experiments on synthetic and realworld graphs suggest that we improve upon competing algorithms for graphs with spectral gaps bounded away from zero.
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