but what happens if we remove one of the konigsberg bridges?one of these so-called eulerian paths in the network. now, a second way in which you can also have an eulerian path is if all the vertices have even degree. in this case, the path will begin and end at the same vertex, and it's a cycle, or an eulerian cycle. but since all the nodes of the original konigsberg bridges are with o degree, we can't complete either the lerian cycle or the eulerian path. ler gave us way to talk about graphs that can be used to express today's networks mathematically. and we can begin to see how his theories are so important to the highly connected world that we live in today, even with something as basic as a municipality planning its snowplow routes. intersections are nodes on this graph and the streets are the edges, and as the plow finishes one street and hits the intersection, it starts plowing down another street. and when it does, it leaves the intersection, as long as the intersection has even degree. that would mean that there's another edge coming in