Information Society and Theory of Hypergraph Formation

In an information society, people acquire information by forming a network or joining in associations. A set of associations is called a hypergraph. It is a generalization of a graph (or a network) in graph theory. While a link in a network directly connects only a pair of nodes, an association in a hypergraph connects any number of nodes. While a link in a network can be formed by the joint decision of two players, an association in a hypergraph can be formed by the joint decision of any number of players more than one. Despite many advantages, forming a network has a disadvantage of exponentially increasing connection costs as the number of society members grow. Alternatively, founding associations has an advantage of saving the cost relevant to the size notwithstanding a high initial setup cost. Once it is established, all members who join in the association can share all the information among the members. In this paper, I examine the conditions for efficiency and stability of a network and a hypergraph, and compare the efficiency between a network and a hypergraph. The main difference is that the possibility of overconnectivity does not occur in a hypergraph, while it occurs in a network. The possibility of overconnectivity in network formation is due to the possible coordination failure. Since coordination by more than two people is allowed in a hypergraph, a hypergraph is never overconnected