Construction of Networking Game for Addressing Social Isolation in a Super-Aging Society - Innovative Management in Information and Production - page 348

The small world presented by Watts has the following characteristics:

1. The number of links is small in proportion to the total number of nodes
(a distributed graph where all the nodes are not mutually connected directly).
2. The distance between any two nodes is short (similar to a random graph with the
same number of nodes).
3. Many nodes are in a cluster form.

The first characteristic can generally be found in networks beyond a certain size
(an employee of a company with 10,000 employees does not directly know all
of his/her colleagues). On this presumption, (2), which is a feature of a random
network, contradicts (3), which is a feature of a regular network. In the small world,
however, they can coexist.

3.4 Creating Hubs by Growth and Preferential Attachment

A scale-free network can be built by means of what is termed growth and
preferential attachment. Simply put, this is a characteristic of the network to prefer
a node with more links to a node with less links, when adding new links for
growth. For example, people tend to select large, popular Web sites when selecting
portal sites (an example of network externality). Snow crystals grow larger as large-
sized crystals absorb surrounding water molecules and smaller crystals. Space dust
amalgamates to create new stars and asteroids. A cluster of small rivers creates a
large river. These are all examples of preferential attachment. It may, in fact, be
seen as a general law of the universe.
The same characteristic lies behind such phenomena as the rich get richer or
increasing returns. It is not an equal world. The growth of links based on the power
law is not limited to the Internet but has been noted in such diverse natural processes
as cell coupling, AIDS infection, the size of earthquakes, the growth of crystals,
and the formation of rivers and applied in economic theory, including the social
scientific analysis of pricing and consumer behavior. The purpose of our study is
to apply the scale-free network concept to communication involving the elderly
and to address their social isolation. Here the concept implies that a given hub will
typically expand as the number of people in the community increases. We may then
investigate how to expand such a hub in terms of a scale-free network, aware of
the fact that social isolation typically increases when a person is not connected with
someone performing the role of a hub.
Figure 7 shows the process of creating such a scale-free network, where each
node of the network corresponds to a person and a link between two nodes enables
the two persons to communicate with each other. The figure shows the gradual
process of nodes (hubs) being created, beginning with no hub at all. The structure of
the scale-free network is designed in such a way that links emerging from nodes are