Isomorphic Graphs: Definition and Examples

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Explores interlacing families, Ramanujan graphs, and their construction using signed adjacency matrices.

Explores the convergence of random walks on graphs and the properties of weighted adjacency matrices.

Explores interlacing families of polynomials and 1-sided Ramanujan graphs, focusing on their properties and construction methods.

Explores graph theory in brain connectomics, MRI applications, network analysis relevance, and individual fingerprinting.

Distinguishes between subgraphs and induced subgraphs in graph theory, illustrating the construction of minimal spanning trees.

Introduces elementary graph algorithms, focusing on Breadth-First Search and Depth-First Search.

Introduces the basics of graphs and networks, covering definitions, paths, trees, flows, circulation, and spanning trees.

Explores pseudorandomness and the Expander Mixing Lemma in the context of d-regular graphs.

Explores distances on graphs, cut norms, spanning trees, blockmodels, metrics, norms, and ERGMs in network data analysis.