An example graph, with 6 vertices, diameter 3, connectivity 1, and algebraic connectivity 0.722
The algebraic connectivity (also known as Fiedler value or Fiedler eigenvalue after Miroslav Fiedler) of a graph G is the second-smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of G.[1] This eigenvalue is greater than 0 if and only if G is a connected graph. This is a corollary to the fact that the number of times 0 appears as an eigenvalue in the Laplacian is the number of connected components in the graph. The magnitude of this value reflects how well connected the overall graph is. It has been used in analyzing the robustness and synchronizability of networks.
^Weisstein, Eric W. "Algebraic Connectivity." From MathWorld--A Wolfram Web Resource.
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the algebraic connectivity is bounded above by the traditional (vertex) connectivity of the graph, algebraicconnectivity ≤ connectivity {\displaystyle...
for his contributions to linear algebra, graph theory and algebraic graph theory. His article, "AlgebraicConnectivity of Graphs", published in the Czechoslovak...
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric...
(2010), "Sentence Connectives in Formal Logic", Stanford Encyclopedia of Philosophy (An abstract algebraic logic approach to connectives.) John MacFarlane...
universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure...
In algebraic topology, homotopical connectivity is a property describing a topological space based on the dimension of its holes. In general, low homotopical...
the shortest cycle Vertex connectivity, the smallest number of vertices whose removal disconnects the graph Edge connectivity, the smallest number of edges...
empirical sciences. Algebra is the branch of mathematics that studies algebraic operations and algebraic structures. An algebraic structure is a non-empty...
center hypervoxel, which is not included in the connectivity. Subtracting 1 yields the neighborhood connectivity, G G = V − 1 {\displaystyle G=V-1} Consider...
are themselves strongly connected. It is possible to test the strong connectivity of a graph, or to find its strongly connected components, in linear time...
C1 and to some vertex in C2. The minimal (a,b)-separators also form an algebraic structure: For two fixed vertices a and b of a given graph G, an (a,b)-separator...
connection between his algebra and logic was later put on firm ground in the setting of algebraic logic, which also studies the algebraic systems of many other...
synchronized" with a remote transmitter uses a phase-locked loop. Algebraicconnectivity Coherence (physics) Kuramoto model Synchronization (alternating...
In algebraic topology, homological connectivity is a property describing a topological space based on its homology groups. X is homologically-connected...
In algebraic topology, a branch of mathematics, a connective spectrum is a spectrum whose homotopy sets π k {\displaystyle \pi _{k}} of negative degrees...
Boolean algebra De Morgan algebra First-order logic Heyting algebra Lindenbaum–Tarski algebra Skew Boolean algebraAlgebraic normal form Boolean conjunctive...
however, and thus the output sets A and B must be an ε-halving. Algebraicconnectivity Zig-zag product Superstrong approximation Spectral graph theory...
done in algebraic semantics. The algebraic semantics of intuitionistic logic is given in terms of Heyting algebras, compared to Boolean algebra semantics...
extension Degree of an algebraic number field, its degree as a field extension of the rational numbers Degree of an algebraic variety Degree (graph theory)...
area. Fan Chung's study in the spectral graph theory brings this “algebraicconnectivity” of graphs into a new and higher level. Chung's work in random graph...
gap. The second smallest eigenvalue of L (could be zero) is the algebraicconnectivity (or Fiedler value) of G and approximates the sparsest cut of a graph...
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