The Laplacian spectrum of graphs

By M. Newman. 2001

1,319 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b28544a8d4bf5d24e70689730a11ed01feafef3e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Coordination of groups of mobile autonomous agents using nearest neighbor rules (2002, background): “In addition to these modeling and simulation studies, research papers focusing on the detailed mathematical analysis of emergent behaviors are beginning to appear.”
Distributed LQR Design for Identical Dynamically Decoupled Systems (2008, background): “We refer the reader to [26] for a more detailed discussion on the importance of the second smallest eigenvalue of a Laplacian.”
Consistency of spectral clustering (2008, background): “Pollard [38] shows consistency of the global minimizer of the objective function for k -means clustering.”
Consensus and Cooperation in Networked Multi-Agent Systems (2007, background): “Graph Laplacians and their spectral properties [29, 58, 55, 32] are important graph-related matrices that play a crucial role in convergence analysis of consensus and alignment algorithms.”
Distributed Parameter Estimation in Sensor Networks: Nonlinear Observation Models and Imperfect Communication (2008, background): “We consider a very generic model of temporally independent link failures, whereby it is assumed that the sequence of network Laplacians,{L(i)}i≥0 are i.i.d. with meanL and satisfyingλ2(L) > 0.”
The von Neumann Entropy of Networks (2008, background): “(See [27] for a survey on Laplacian spectra.”
A connection between ordinary and Laplacian spectra of bipartite graphs (2008, background): “The multiplicity of the Laplacian eigenvalue zero of the graph G is equal to the number of its connected components [8,9].”
A tutorial on spectral clustering (2007, background): “The unnormalized graph Laplacian and its eigenvalues and eigenvectors can be used to describe many properties of graphs, see Mohar (1991, 1997).”
Multi-View Clustering and Semi-Supervised Classification with Adaptive Neighbours (2017, background): “There is an important property of Laplacian matrix (Mohar 1991), (Chung 1997) Theorem 1.”
Distributed Consensus Algorithms in Sensor Networks: Quantized Data and Random Link Failures (2007, methodology): “Throughout the paper the symbolsP[·] andE[·] denote the probability and expectation operators w.r.t. the probability space of interest.”
Graph Learning for Multiview Clustering (2018, unknown): “GRAPH LEARNING If all the elements in the similarity matrix S ∈ Rn×n are nonnegative, its Laplacian matrix L has the property [33], [34].”
An efficient method for decomposition of regular structures using graph products (2004, methodology): “Mohar [8] has applied ( 2, v2) to different problems such as graph partitioning and ordering.”
Broadcast Gossip Algorithms for Consensus (2009, background): “A result of Mohar [37] gives this lower bound in terms of the diameter of the graph.”
Random Walks on Simplicial Complexes and the normalized Hodge Laplacian (2018, background): “As network-based system models have become almost ubiquitous across scientific domains [20,93], graphs and their Laplacians feature prominently in many analysis tasks [9, 12, 40, 64, 87, 89].”