Algebraic connectivity of graphs
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This article is published in Czechoslovak Mathematical Journal.The article was published on 1973-01-01 and is currently open access. It has received 3888 citations till now. The article focuses on the topics: Algebraic graph theory & Irreducible component.read more
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Graph-based interpretation of the molecular interstellar medium segmentation
D. Colombo,Erik Rosolowsky,Adam Ginsburg,Ana Duarte-Cabral,Annie Hughes,Annie Hughes,Annie Hughes +6 more
TL;DR: The method designed, SCIMES (Spectral Clustering for Interstellar Molecular Emission Segmentation) considers the dendrogram of emission in the broader framework of graph theory and utilizes spectral clustering to find discrete regions with similar emission properties.
Journal ArticleDOI
Uncovering the overlapping community structure of complex networks by maximal cliques
TL;DR: A unique algorithm is proposed to detect overlapping communities in the un-weighted and weighted networks with considerable accuracy and successfully finds overlapping vertices and bridge vertices between communities.
Posted Content
Nearly-Linear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems
TL;DR: A randomized algorithm is presented that on input a symmetric, weakly diagonally dominant matrix A with nonpositive off-diagonal entries and an n-vector produces an x such that $\tilde{x} - A^{\dagger} {b} \leq \epsilon$ in expected time.
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On the Smallest Eigenvalue of Grounded Laplacian Matrices
Mohammad Pirani,Shreyas Sundaram +1 more
TL;DR: In this paper, the smallest eigenvalue of grounded Laplacian matrices was shown to approximate the convergence rate in consensus dynamics with stubborn or leader nodes, and the smallest Eigenvalue for weighted Erdos-Renyi random graphs with a single row and column removed.
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Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks
TL;DR: This dynamic framework creates a systematic link between different stochastic dynamics and their corresponding notions of optimal communities under distinct (node and edge) centralities and shows that the Markov Stability can be computed efficiently to find multi-scale community structure in large networks.
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Book ChapterDOI
Congruent Graphs and the Connectivity of Graphs
TL;DR: In this paper, the authors give conditions that two graphs be congruent and some theorems on the connectivity of graphs, and conclude with some applications to dual graphs, which can also be proved by topological methods.