In today's lecture we continued learning about the Mathematics of Networks. We first learnt what a path is and continued with different types of paths. Self-avoiding paths do not intersect themselves. While tracing a path we must be careful if the edges are directed. Shortest path is the shortest sequence of links connecting two nodes. We also learnt how to calculate the path length (L), average path length (N) and diameter (D) of a network. According to formulas, we can get the relation between them as 1< L<= D< N. Two known types of paths Eulerian and Hamiltonian differ in one way. Hamiltonian path is always self-avoiding because it visits each vertex exactly once. However being self-avoiding of a Eulerian path depends on the degrees of vertices.
Another metric of a network is components. In weakly connected components every node can be reached from every other node. In strongly connected components each node must be reached from every other node within the component.
Final thing that is covered is the eigenvalues and eigenvectors. We calculated the eigenvalues and eigenvectors of a matrix from the given formulas.
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