برنامه های کاربردی شبکه های جهان کوچک برای برخی از سیستم های اجتماعی و اقتصادی

Small-world networks (SWN) are found to be closer to the real social systems than both regular and random lattices. Then, a model for the evolution of economic systems is generalized to SWN. The Sznajd model for the two-state opinion formation problem is applied to SWN. Then a simple definition of leaders is included. These models explain some socio-economic aspects

The diffusion of a new concept (a technology, an opinion, an information, a disease, ...) through social and economic systems is a complex process that typically forms waves or avalanches. Also, it usually displays rich dynamics that is attracting the interest of many mathematicians and theoretical physicists [1]. A social network has two main properties: clustering and small-world effect. Clustering means every one has a group of collaborators, some of them will often be a collaborator by another person. Small-world effect means the average shortest person to person (vertex to vertex) distance is very short compared with the whole size of the system (number of vertices). Regular lattices display the clustering property only. On the other hand, random lattices display the small-world effect without clustering [2]. The concept of SWN introduced in [2] and [3] has shown to combine both features. A SWN is a connected ring with some shortcuts joining between some randomly chosen vertices are added with small probability φ. Also, this structure combines between both local and nonlocal interactions. This combination is observed in many real systems. Then it is a useful concept in modeling the real systems. We used this concept in modeling different systems [4], [5], [6], [7] and [8]. Here our interest is restricted to apply the concept of SWN to a model for the evolution in economic systems [8] and to a sociophysics model [7].

In conclusion, SWN is a good description for real social networks. It allows some simple mathematical models to display some interesting socio-economic aspects.