Does graph theory predate computer science?

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I am curious if mathematicians came up with the idea of Graph Theory (the study of pairwise relationships between objects visualized as nodes connected by edges) before the field of Computer Science necessitated it? Or was Graph Theory a natural consequence of Computer Science born out of the need to visualize/evaluate large and complex pairwise relationships?

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The Königsberg bridge problem was solved by Euler in 1736, whereas Charles Babbage was born in 1791.