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Instructions
This Java applet (If you don't see anything above, please install Java 1.4) visualizes the model presented in Modeling Dynamics of Information Networks by Martin Rosvall at Umeå University and Kim Sneppen at NORDITA (Phys. Rev. Lett., 91:178701 (2003)). See also the presentation given at the Niels Bohr Summer Institute on Complexity and Criticality, 21 - 30 August 2003. In this Java applet, a small and fixed number (100) of
agents (nodes) are connected by some adjustable (or adaptive) number of
links (more than 99 to keep the network connected). To change the
value, just type a new value and press enter. In the network to the
left, nodes are attracted to the center when they have many links to
visualize the rise and fall of hubs of different sizes. The right
figure shows the degree (number of links per node) of the largest and
next largest hub. Every agent has a memory that corresponds to a rough picture
of the network. The memory consists of an estimated shortest path
length to any other agent in the network and the direction of the path
in the form of the nearest neighbor on the corresponding path. By
successive rewiring attempts the agents try to optimize their
positions, that is, minimizing the distances to other agents. After a
successful rewiring the agents in the local neighborhood of the
rewiring (3 agents are involved) are allowed to "chat" with each other
to update their information of the network. The conversation
corresponds to a comparison of a fraction S of the two nearest
neighbors' memories. If a neighbor provides shorter paths to some
agents, the agents adapt the new paths. The correctness of the
information the agents have about the system can accordingly be
adjusted by the parameter S (0 < S < 1). A small S results in bad
information and the rewiring is close to random and no agent can
survive as a hub with many links for a long time. A high S results in
good information, the agents' memories give a good picture of the
network, and an agent can survive as a hub for a long time since this
topology minimizes the path lengths for agents in the network. The number of links in the network play a similar role as
the information exchange rate S. With many links in the system the
agents suffer from their limited information horizon and get messed up
by all the links. With added links an increased S is accordingly
necessary to obtain a similar topology as for a network with less
links. On a transition line between the chaotic, highly dynamic and
"confused" state (typically low S and many links) and the ordered and
one-hub dominated frozen state (typically high S and few links)
the degree distribution
is broad, in fact of scale-free form. Scale-free degree distribution
means that the probability to find a randomly chosen node with k links
follows a power-law. For a given S, the number of links that give the network
scale-free degree distribution is attained by letting the total number
of links fluctuate in the following way: When one hub dominates the
topology, links are added and when no hub dominates, links are deleted.
The dominance of a hub is here measured as the fraction of the number
of links of the largest and next largest hub in the network. For
example, when the "SOC" button above is pressed a link is created at a
low rate with a probability Pc proportional to the ratio between the
highest and next highest degree in the network and deleted with the probability 1-Pc. When pressing the button "Namedrop" one randomly chosen
agent, markt green, will constantly allow all its neighbors to update
their information by using his information. This agent will soon become
the major hub in the system. Thus, communication is the key to success
in this model. |
Philosophy
Life without information is not life. From the genetic blueprint in our DNA to the world-wide Internet, information and its dynamic counterpart communication define our civilization. However, we live under the limited information horizon, in the sense that information is often imperfect and communication is always finite. In a society the information horizon is set by each individual's social contacts, which in turn is a part of the global network of human communication. One simple goal for individuals is to be central. Thus we model a society where players try to be as close as possible to everybody else by moving their social connections. Local communication gives rise to global organization. Communication and not correctness appears as a success-strategy for individuals. In other words we explore the local dynamic origin of global network organization by modeling response to information transfer in a simplified social system. The scenario is a set of players, that each tries to be as close as possible to everybody else. The players adjust their social connections to achieve this goal, guided by a limited knowledge about the individual players' positions in the network. The finite information is in turn obtained by local communication. When local communication is weak, the system disorganizes into a highly dynamic and chaotic network where no single player is dominating the system. In network language, the degree distribution is narrow, or in technical words exponential. On the other hand, when local communication is strong, the system organizes into a coherent structure dominated by a central hub that remains indefinitely frozen. In between, there is a critical transition in the dynamics where no hubs take over for ever, and where at the same time the network has players with all types of connectivities. The network is scale-free and furthermore hierarchical, in a way that resembles the Internet and often social and biological networks. The modeled society opens for investigation of the interplay between individual behavior and global organization, as well as for exploring possible success-strategies for individuals. For example, we find that scale free-networks may be associated to a dynamics on the edge of chaos. In fact, the system can self-organize to this transition between the frozen and the disordered state by a simple feedback mechanism associated to just the two most connected players in the system. Another interesting feature is that the success of individuals appears to not so much depend on their correctness, but rather on their ability to communicate actively. A talkative player's boasting is a self prophecy in the sense that it will lead it to become a major player in the system. Name-dropping pays off, also in a simulated society.
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