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  "body": "\n## Summary\n\nThe effective resistance between two vertices of an [[electrical network|T7KRE7J3B4]] is the resistance of the whole network seen from those two vertices.\nIt is the voltage difference needed to push a unit current from one vertex to the other.\nIt is a metric on the vertices, called the resistance distance, and it can be computed from the pseudoinverse of the [[graph Laplacian|TN6M6DVZRP]].\nFor random walks it gives escape probabilities, commute times and criteria for recurrence.\n\n## Explanations\n\n### L1 human\n\nReplace the whole network between $a$ and $b$ by a single resistor that behaves the same way from the outside: its resistance is the effective resistance.\nResistors in series add: two unit resistors in a row have effective resistance $2$.\nResistors in parallel combine by adding conductances: two unit resistors side by side have effective resistance $\\tfrac12$.\nMany paths between $a$ and $b$ make the effective resistance small, and a single long path makes it large.\n",
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