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-theoretic connectivity control of mobile robot networks
TL;DR: In this paper, a graph-theoretic definition of connectivity is provided, as well as an equivalent definition based on algebraic graph theory, which employs the adjacency and Laplacian matrices of the graph and their spectral properties.
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The ab-initio density matrix renormalization group in practice
Roberto Olivares-Amaya,Weifeng Hu,Naoki Nakatani,Naoki Nakatani,Sandeep Sharma,Jun Yang,Garnet Kin-Lic Chan +6 more
TL;DR: By examining a diverse benchmark set of molecules, including π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, some answers are provided to questions about the density matrix renormalization group and how it is used in practice.
Journal Article
Proto-value Functions: A Laplacian Framework for Learning Representation and Control in Markov Decision Processes
Sridhar Mahadevan,Mauro Maggioni +1 more
TL;DR: A novel spectral framework for solving Markov decision processes (MDPs) by jointly learning representations and optimal policies is introduced, and several strategies for scaling the proposed framework to large MDPs are outlined.
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Multi-Agent Coordination by Decentralized Estimation and Control
TL;DR: A framework for the design of collective behaviors for groups of identical mobile agents based on decentralized simultaneous estimation and control is described, which derives conditions which guarantee that the formation statistics are driven to desired values, even in the presence of a changing network topology.
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Abrupt transition in the structural formation of interconnected networks
Filippo Radicchi,Alex Arenas +1 more
TL;DR: In this paper, a model of an interdependent network of networks is presented, and it is shown that an abrupt phase transition occurs when interconnections between independent networks are added.
References
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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.