What is spectral graph theory used for?

What is spectral graph theory used for?

Spectral graph theory gives an expression of the combinatorial properties of a graph using the eigenvalues and eigenvectors of matrices associated with the graph. These ideas were first introduced in the late 80s in order to prove Cheeger’s inequality for finding a sparse cut.

Is a spectrum a graph?

The spectrum of a graph may be computed in the Wolfram Language using Eigenvalues[AdjacencyMatrix[g]]. Precomputed spectra for many named graphs can be obtained using GraphData[graph, “Spectrum”]. A graph whose spectrum consists entirely of integers is known as an integral graph.

What graphs are determined by the spectrum?

In the Wolfram Language, graphs known to be determined by their spectra are identified as GraphData[“DeterminedBySpectrum”].

What is lambda in graph theory?

In applied mathematics, lambda-connectedness (or λ-connectedness) deals with partial connectivity for a discrete space. Assume that a function on a discrete space (usually a graph) is given. A degree of connectivity (connectedness) will be defined to measure the connectedness of the space with respect to the function.

Who introduced spectral graph theory?

Discrete geometric analysis created and developed by Toshikazu Sunada in the 2000s deals with spectral graph theory in terms of discrete Laplacians associated with weighted graphs, and finds application in various fields, including shape analysis.

What is graph signal processing?

Graph signal processing is an active research area in recent years resulting in many advanced solutions in various applications. In numerous practical cases the signal domain is not a set of equidistant instants in time or a set of points in space on a regular grid.

What is Lambda G in graph?

Definition 9.3: The connectivity number λ(G) is defined as the minimum number of edges whose removal from G results in a disconnected graph or in the trivial graph (=a single vertex). A graph G is said to be k-edge-connected if λ(G) ≥ k.

What is the difference between Euler path and Euler circuit?

An Euler path is a path that uses every edge of a graph exactly once. An Euler circuit is a circuit that uses every edge of a graph exactly once. ▶ An Euler path starts and ends at different vertices.

What are two types of spectrum?

The spectra can be divided into two types viz., emission and absorption spectra.

What is signal processing used for?

Signal processing manipulates information content in signals to facilitate automatic speech recognition (ASR). It helps extract information from the speech signals and then translates it into recognizable words.

What is a signal plot?

The Signal Plot feature uses signal groups, or collections of signals, to plot. New groups can be created by clicking on the button, or removed using the button (Figure 1: ). Signal groups are edited by clicking the Select Signals button and using the Expression Builder.

What is isolated vertex?

An isolated vertex is a vertex with degree zero; that is, a vertex that is not an endpoint of any edge (the example image illustrates one isolated vertex). A leaf vertex (also pendant vertex) is a vertex with degree one.

What is the difference between Euler and Hamiltonian path?

An Euler path is a path that passes through every edge exactly once. If it ends at the initial vertex then it is an Euler cycle. A Hamiltonian path is a path that passes through every vertex exactly once (NOT every edge).