General algebraic connectivity
Web15. The most common measures of connectivity are edge-connectivity and vertex-connectivity. The vertex-connectivity, or just connectivity, of a graph is the minimum … WebThe algebraic connectivity of a connected undirected graph is the second smallest eigenvalue of its Laplacian matrix. An undirected graph. The data key used to determine the weight of each edge. If None, then each edge has unit weight. Whether the normalized Laplacian matrix is used. Tolerance of relative residual in eigenvalue computation.
General algebraic connectivity
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WebAlgebraic connectivity, the second smallest eigenvalue of the graph Laplacian matrix, is a fundamental performance measure in various network systems, such as multi-agent networked systems. Here, we focus on how to add an edge to a network to increase network connectivity and robustness by maximizing the algebraic connectivity. Most efficient … Web图 的 代数连通度 （algebraic connectivity）是 的 拉普拉斯矩阵 的第二小的 特征值 （重特征值要重复计算）。. [1] 这个特征值大于0当且仅当 是 连通图 。. 这是一个简单的推 …
WebJul 25, 2024 · The algebraic connectivity of a graph $G$ is defined as the second smallest Laplacian eigenvalue of the graph and is denoted by $a(G)$. It is known … WebApr 10, 2024 · For the conventional linear protocols, researchers endeavored to find proper interaction graphs with larger algebraic connectivity to get high convergence rate [15, 20]. Nevertheless, they had not found any available protocol to make consensus occur within finite time. ... as the general algebraic connectivity of \(\mathcal {G}(\varvec{A})\) ...
http://www-scf.usc.edu/~hoyeeche/papers/connectivity_conf.pdf http://www.momo.cs.okayama-u.ac.jp/~takahashi/pdf/ieeetcones2024accepted.pdf
WebMar 15, 2024 · By definition, the vertex connectivity is always an integer, while the algebraic connectivity is an integer or an irrational number. In cases in which the difference between them is an integer, the algebraic connectivity must be an integer. Thus, we study families of Laplacian integral graphs (all the Laplacian eigenvalues are …
WebMar 15, 2024 · Absolute algebraic connectivity. Find edge weights that maximize the algebraic connectivity of the graph (i.e., the smallest positive eigenvalue of its … local weather nags head ncWebThe algebraic connectivity, denoted as μN − 1, is the smallest non-zero eigenvalue of Q, which is greater than zero if and only if the graph G is connected. From a robustness standpoint, the magnitude of μN − 1 reflects how many nodes should be removed in order to disconnect a graph [ 19 ]. The larger the algebraic connectivity is ... local weather naplesWebApr 15, 2015 · A nice recent survey on algebraic connectivity is . In general, the problem of finding the optimal graph given m edges and n vertices is known to be NP-complete . Despite this fact, several simple heuristics exist that can be used to obtain a graph with reasonably large algebraic connectivity , . local weather myrtle beach south carolinaWebMay 1, 2007 · This paper is a survey of the second smallest eigenvalue of the Laplacian of a graph G, best-known as the algebraic connectivity of G, denoted a(G).Emphasis is … local weather n18WebThe algebraic connectivity of a graph is one of the most well-studied parameters in spectral graph theory. It is de ned as the second smallest eigenvalue of the combinatorial … local weather napervilleWebJan 1, 2015 · At first, consensus can be reached if the general algebraic connectivity exceeds a particular value associated with the coupling strengths and the positive left … local weather naples maineWebJun 1, 2015 · By introducing two notions of general algebraic connectivity, a detailed analysis has been performed to reach global synchronization. At the same time, the case of infinitely frequent triggering is excluded by showing that the inter-event interval is strictly larger than a positive low bound. It is found that some existing results can be seen ... local weather mystic ct