The algebraic connectivity of a graph, also known as its Fiedler value after Miroslav Fiedler, is the second smallest eigenvalue of the Laplacian matrix of the graph, counting repeated eigenvalues separately. This eigenvalue is greater than zero if and only if the graph is connected, since the number of times zero appears as a Laplacian eigenvalue equals the number of connected components the graph has. The magnitude of the algebraic connectivity reflects how well connected the graph is overall, and it has been used to analyze the robustness and synchronizability of networks. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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1. Algebraic connectivity (Wikipedia)
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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. This eigenvalue is greater than 0 if and only if G is a connected graph.
In Branch: Graph Theory, Lead paragraph
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.
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