Finally, we compare our method with existing approaches and relate the hitting probability metrics and effective resistance in a stochastic case. In particular, the effective resistance captures the commute and covering times for strongly connected weight balanced directed graphs. Each entity is represented by a Node (or vertice). Although the effective resistance of our proposal is asymmetric, we prove that it induces two novel graph metrics in general strongly connected directed graphs. A directed graph is graph, i.e., a set of objects (called vertices or nodes) that are connected together, where all the edges are directed from one vertex to another. Network diagrams (or Graphs) show interconnections between a set of entities. In addition, we generalize the effective resistance to a directed graph using Markov chain theory, which is invariant under a Kron reduction. Furthermore, we prove that this reduction method preserves the structure of the original graphs, such as the strong connectivity or weight balance. In this study, we propose a generalization of a Kron reduction for directed graphs. Although these two graph-theoretic concepts stem from the electric network on an undirected graph, they also have a number of applications throughout a wide variety of other fields. In addition, the Kron reduction method is a standard tool for reducing or eliminating the desired nodes, which preserves the interconnection structure and the effective resistance of the original graph. In network theory, the concept of effective resistance is a distance measure on a graph that relates the global network properties to individual connections between nodes. 4 Line Graphs 4.1 Making a Basic Line Graph 4.2 Adding Points to a Line Graph 4.3 Making a Line Graph with Multiple Lines 4.4 Changing the Appearance of Lines 4.5 Changing the Appearance of Points 4.6 Making a Graph with a Shaded Area 4.7 Making a Stacked Area Graph 4.8 Making a Proportional Stacked Area Graph 4.
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