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" Euler's proof that in Konigsberg there is no path crossing all seven bridges only once was based on a simple observation. Nodes with an odd number of links must be either the starting or the end point of the journey. A continuous path that goes through all the bridges can have only one starting and one end point. Thus, such a path cannot exist on a graph that has more than two nodes with an odd number of links. As the Konigsberg graph had four such nodes, one could not find the desired path. "

Albert-László Barabási , Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life


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Albert-László Barabási quote : Euler's proof that in Konigsberg there is no path crossing all seven bridges only once was based on a simple observation. Nodes with an odd number of links must be either the starting or the end point of the journey. A continuous path that goes through all the bridges can have only one starting and one end point. Thus, such a path cannot exist on a graph that has more than two nodes with an odd number of links. As the Konigsberg graph had four such nodes, one could not find the desired path.