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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The ordering of trees and connected graphs by algebraic connectivity
TL;DR: In this article, the first four trees of order n ⩾ 9 with the smallest algebraic connectivity are P n, Q n, W n and Z n with α (P n ) α (Q n ), α (W n ) = α ( Q n ), W n, W n, and W n ).
Journal ArticleDOI
Geometry of Complex Networks and Topological Centrality
Gyan Ranjan,Zhi-Li Zhang +1 more
TL;DR: In this article, the authors explore the geometry of complex networks in terms of an n -dimensional Euclidean embedding represented by the Moore-Penrose pseudo-inverse of the graph Laplacian (L + ).
Proceedings ArticleDOI
Robustness and vulnerability analysis of water distribution networks using graph theoretic and complex network principles
Alireza Yazdani,Paul Jeffrey +1 more
TL;DR: Two metrics of meshed-ness and algebraic connectivity are proposed as candidates for quantification of redundancy and robustness, respectively, in optimization design models and a brief discussion on the scope and relevance of the provided measurements in the analysis of resilience of water distribution networks is presented.
Journal ArticleDOI
Framework for measuring complexity of aerospace systems
TL;DR: A measure that incorporates size, coupling, and modularity aspects of complexity is developed that emphasizes the importance of indirect coupling and feedback loops in the system and is found to be scalable for large-scale systems involving thousands of components and interactions.
Journal ArticleDOI
Detecting community structure via the maximal sub-graphs and belonging degrees in complex networks
TL;DR: This paper proposes a new algorithm to detect overlapping community structure in complex networks and extends the modularity function to evaluate the proposed algorithm, which gives satisfactory results.
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.