International Encyclopedia of Systems and Cybernetics

A structure of communication links that allows for exchanges of energy, matter and/or information among the elements (processors) or subsystems in a system.

Basically, networks are: a) combinatorial, according to rules;

b) auto-catalytic by spontaneous construction of functional cycles.

Normally, each processor acquires a specific activity, i.e. specific links with other processors, which either act upon it, or are acted upon by it. This is why networks are easily represented by graphs, and particularly, oriented ones.

As noted by J.A. GOGUEN and F.J. VARELA, the network model is closely related to the concept of recursion, but in opposition to the restricted vertical concept of hierarchy: "The reciprocal connectivity of a net suggests the coordination of a system's elements; a tree structure suggests the sequential subordination of a system's parts, each part having its own well defined input-output behavior description ". Consequently, these autors define a network as "a directed graph" (1979, p.36).

Any network must be pre-defined by appropriate constraints, i.e. a selection of the actual or potentially useful links, excluding those who should not be significant for a proper working of the system.

L.H. KAUFFMAN states: "A slight disturbance creates conditions of local imbalance through the net. The net preserves itself by correcting these imbalances, but in the process may create further imbalances" (1977, p.179) and… "… networks… are characterized by a self-referential interdependence of parts and the whole. The behavior is a matter of balance among the parts and the preservation of this balance under internal and external perturbations" (p.187).

Starting with an initial situation and quite simple rules, many systems generate themselves by constructing their own intercommunication network through a progressive process of trial and error, applied to succesive inputs. See: "Genetic algorithms; order from noise; Boolean functions".

Conversely however, networks are difficult to program in the habitual sense, because the introduction of a ready made algorithm should inhibit their self training ability.

On the contrary, processes of self-training appear to be at work within the learning brain, the perceptron and the more recent so-called neural computers, as well as societies (human, ecological, and probably of robots in a not too distant future)

Nets elements work in parallel. Thus, at the same instant, many different events happen within the network. This leads to chaotic determinism in the behavior of the system.

A network has generally very numerous potential states implicit in the multiple possible combinations of its elements.

St. KAUFFMAN states that "Because all the elements act simultaneously, the system is… said to be synchronous. A system passes from one unique state to another. The succession of states is called the trajectory of the network" (1993, p.66).

Moreover networks have a finite number of states: "A system must therefore eventually reenter a state that it has previously encountered" (Ibid.).

This should possibly be somewhat qualified: Very complex systems have so many possible states that they may practically never reenter again a former state, while however some of its stable parts ("frozen cores" in KAUFFMAN's terminology) may do.

Once the network is organized, i.e. has acquired some specific function, this function responds to a matrix of state transitions.

Closely related subjects are: "Connectionism", "Constructivism" and "Neural networks".