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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]] and let $v$ be a vertex of $G$ with a finite [[neighbourhood|01T3TMGTTE]] $N(v)$.\nThe degree of $v$ is the number\n$$\\deg(v) = |N(v)|$$\nof vertices adjacent to $v$. It is also the number of edges that contain $v$.\n\n## Remarks\n\nA vertex of degree $0$ is isolated, and a vertex of degree $1$ is a leaf.\nA graph is locally finite when each vertex has finite degree. Each finite graph is locally finite.\nIn a [[multigraph|01M5T0KDG7]], the degree counts edges with multiplicity, and a loop counts twice.\n\n## Explanations\n\n### L1 human\n\nThe degree of a vertex is the number of edges at that vertex.\nIn a friendship graph it is the number of friends of a person.\n",
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