Like 7 bridge problem, graph theory is a study of how nodes in the network connect to each other in the most efficient way. Two primary factors in the graph are vertices and edges. In this modern age, we are interested in information networks, which is the network moving information from one node to another. There are some terminologies that we might need to know before we go further to the detail of networks. First, collaboration graph visualize how people cooperate with each other, linking every pair together if they cooperate with each other. Path is a sequence of path that link nodes. In the Internet, we choose the shortest path/minimum path, which goes through the least number of nodes.
We also interpret graph by degree of network, which is the number of link connecting to a node. The more degree the more strength the connectivity is. Divided by network direction, degree include indegree, request from others, and outdegree, request to others. The number of nodes in the network is also an important indicator to interpret graph. An inference of degree is the small world phenomenon, which is also known as six degree of separation, defining the whole world graph as a giant component. Using the least numbers of nodes to define the distance between two nodes, the small world experiment found the average degree is around 6 between a person and everybody in the world, that is, we can connect to everyone in the world through 6 people. Interestingly, Facebook revealed that currently the average degree became 5, which means the world becomes closer. Small world phenomenon can be observed when you are looking for a job, but surprisingly, weak ties with less strength connection can help you more than the strength ties.
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