Highlights
id795551798
Euler’s proof that in Königsberg 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 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 Königsberg graph had four such nodes, one could not find the desired path.
id795551799
Euler’s unintended message is very simple: Graphs or networks have properties, hidden in their construction, that limit or enhance our ability to do things with them.
id795551800
In many ways Euler’s result symbolizes an important message of this book: The construction and structure of graphs or networks is the key to understanding the complex world around us. Small changes in the topology, affecting only a few of the nodes or links, can open up hidden doors, allowing new possibilities to emerge.