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A square matrix $A$ where $A_{ij}$ represents the presence (often with a 1) or absence (with a 0) of an edge between vertices i and j in a graph. Used to analyze graph properties and compute eigenvalues that relate to the graph's structure.

The second smallest eigenvalue of the Laplacian matrix of a graph, denoted by $\lambda_2$. It measures how well-connected a graph is. A value greater than 0 indicates the graph is connected.

A technique that uses eigenvectors of a graph's Laplacian matrix to cluster nodes into groups that minimize the number of inter-cluster edges. It is widely used in machine learning for data classification and image segmentation.

An inequality which provides a bound relating the algebraic connectivity (second smallest eigenvalue) of a graph and its edge expansion (Cheeger constant). It is a tool used in understanding the efficiency of network flow and bottleneck issues.

The set of eigenvalues of a graph's adjacency matrix, which provides insights into the graph’s structure. Can be used to determine properties like connectivity, bipartiteness, and graph isomorphisms.

A measure of the influence of a node in a network. It assigns relative scores to all nodes based on the concept that connections to high-scoring nodes contribute more to the score of a node than equal connections to low-scoring nodes.

A value expressing the tightness of a graph's eigenvalues, defined as $R(x) = \frac{x^T A x}{x^T x}$ for a vector $x$. It characterizes various properties of the graph and is used in optimization problems involving eigenvalues.