Analysis of Networks
- / -
Annex 9 of Visualization
of International Relationship Networks
The data collected together in the sections of the Encyclopedia
of World Problems and Human Potential
has been deliberately organized
in a manner which stresses the interrelationships between the entities
within a section and between those in different sections. (Each section
is characterized by entities of a different type, and several types of
relationship may exist between the same two entities). In effect, therefore,
the entities and relationships in each section constitute a network, possibly
composed of many subnetworks. Similarly, since entities in each section
may be linked to those in other sections, the whole is constituted by a
system of interlinked networks in which the relationships have a limited
number of distinct meanings. The entities and relationships are currently
held in computer files in a form which should facilitate analysis of these
networks. It is hoped that the availability of data in this form will encourage
the development of new types of analysis more appropriate to the structural
complexity portrayed, especially since both the quantitative data and the
mathematical functions representing the nature of particular relationships
under different conditions (which are a precondition for the application
of current methods of quantitative analysis of social systems), are absent
and in most cases unavailable.
As François Lorrain notes (1) the abstract notion of a network is
undoubtedly called to play a role in the social sciences comparable to
the role played in physics by the concept of euclidean space and its generalizations.
But the poverty of concepts and methods which can currently be applied
to the study of networks stands in dramatic contrast to the immense conceptual
and methodological richness available for the study of physical spaces.
A whole reticular imagery remains to be developed. At this time a network
is understood to contain simply nodes and links and little else. An attempt
to define anything like a reticular variable results in very little. This
is not surprising, since to succeed would require the establishment of
a general mathematical theory of networks which as yet has been little
developed. In contrast to this situation, consider the multitude of spatial
variables which are available: coordinates, length, surface, volume, curves,
classes of curves, classes of surfaces, parameters of curves, parameters
of surfaces, and so on, and all these in a space of any number of dimensions
and manifesting any type of curvature.
(a) Social networks
: The types of network which occur in the social
sciences are of such a diverse nature that only a purely formal definition
of this notion is of sufficient generality.
A network is constituted by a certain set of points. In the social sciences
these points may represent any or all of the following: individuals, groups,
organizations, beliefs, roles, etc
. In this exercise they represent:
international organizations, multilateral treaties, world problems, strategies,
concepts (human development, integrative, patterns), metaphors, symbols,
modes of awareness, values. Such points may represent the existence of
entities at the present time, or they may represent the existence of entities
at some past or future time (or such points may also be used to represent
intervals of time).
The points in a data set may be linked by one or more kinds of relationship.
In this exercise three basic types of relationship are distinguished:
(i) Simple relationship, namely A is related to B which implies
that B is related to A;
(ii) Hierarchical relationship, namely A is a part of B which
implies that B is in contextual relationship to A;
(iii) Functional relationship, namely A acts on B which implies
that B is acted upon by A.
In the first case above a relationship is further defined by the types
of entity between which it occurs, namely whether they are of the same
type, or whether they are of different types. In the second and third case,
a relationship is further defined by distinguishing the direction of the
relationship, which is further developed in the third case by distinguishing
several ways in which A can act upon B.
(b) Analysis of networks
: Classical mathematics, summarizing François
Lorrain's (1) remarks, is not able to handle complex structural features
characteristic of social systems. Organization is best depicted as a network.
The mathematical theory of networks derives largely from certain branches
of topology and abstract algebra rather than from analysis, which underlies
classical mathematics. The theory of graphs is often presented as a kind
of general theory of networks with numerous possible applications in the
social sciences. However, other than in the area of operations research,
the theory of graphs has not proved itself to be very useful in sociology.
The reason is probably that the theory has mainly been developed in the
context of relatively limited problems in such a way that the results collected
under the graph theory label, although numerous and of great interest,
have little unity. In addition, the theory rarely handles networks with
several distinct types of relationships each with its own configuration
of links. It is precisely such networks which are of most interest in sociology.
The theory also tends to exclude networks in which some of the points have
links back to themselves when it is often just such networks which are
important in representing social structures.
A final disadvantage of the theory of graphs is that it only offers a fairly
limited number of means of global analysis of networks. It seriously neglects
an important aspect of the study of any type of mathematical structure,
namely the level of transformation relations between graphs. Because of
its composition, a category possesses a richerstructure than a simple graph,
and it is therefore possible to define more rigorous and fruitful criteria
of transformation (namely the concepts of function and functional reduction).
In addition a set of points and a set of relations can be treated in their
totality and simultaneously, in contrast to the methods of graph theory
which considers individual paths between particular points in the graph.
In the universe of categories (the universe of objects and relationships),
transformations between categories may also be considered as relationships
within a category whose objects are themselves categories, and so on. All
this emerges from consideration of the global structure resulting from
the manner of composition which relates the relationships themselves, thus
providing a dialectic of levels of structure and a new imagery of networks.
At all levels of this universe, the functional relationships between categories
play a central role. They are the fundamental instruments which may be
used in the exploration of structural complexity and the tools for extraction
of information in global studies.
(c) Use of graph theory methods
: Despite the limitations noted above,
graph theory methods have been applied to the analysis of social structures
although such applications are not very common (see references below).
The image of a "network or web" of problems (or organizations,
) to represent a complex set of interrelationships is a fairly
familiar one. This use of "network", however, is purely metaphorical
and is very different from the notion of a network of concepts as a specific
set of linkages among a defined set of concepts, with the additional property
that the characteristics of these linkages as a whole may be used to interpret
the semantic significance of the concepts involved.
(d) Some features of graphs
: Using graph theory, a number of characteristics
of networks can be determined. Points 1 to 3 below are concerned with the
shape of the network, 4 to 8 with interactions within the network.
(e) Implications of artificial intelligence research
(i) Centrality: A measure (in topological not quantitative terms)
of the extent to which a given entity (eg a problem) is directly
or indirectly "related" via links to other entities (ie,
the extent to which it is "distant" from another entity). One
can speak of a "key" problem or of an organization being "central"
to the concerns of a particular complex. It may also be considered a measure
of the degree of "isolation" of the entity. A systematic analysis
of the centrality of entities in a network could indicate where new entities
are necessary to bridge gaps and link isolated domains.
(ii) Coherence: A measure of the degree of "interconnectedness"
or "density" of a group of entities. This may be considered as
the degree to which a system of problems is "complete". Differences
in density would reflect the tendency for more highly coherent problem
systems to appear more self-reinforcing in comparison to less organized
parts of the network. In some respects this is an indication of the degree
of "development" of a problem system.
(iii) Range: Some entities are directly related to many other
entities, others to very few. The range of an entity is a measure of the
number of other entities to which it is directly related. Range could be
considered an indication of the "vulnerability" of a problem
to the extent that a high range problem would be less vulnerable to attack
than a low range problem, since it has more relationships anchoring it
to its problem environment and preserving it in existence. High range points
are therefore either key points in resistance to problem change or else
key points in terms of which orderly change can be introduced.
(iv) Content: The "content" of a relationship between
entities is the nature or reason for existence of that relationship. Simple
graphs have only one link between any two entities; multigraphs have two
or more links, each of different content.
(v) Directedness: A relationship between two entities may have
some "direction" (ie, A to B, or B to A). There may be
several types of directedness. Two types are important for this project:
A is a sub-element of B; A acts on B. In a multigraph, one link may point
from A to B and the other from B to A.
(vi) Durability: A measure of the period over which a certain
relationship between entities is activated and used. At one extreme, there
are the links activated only on a "one-shot" basis (eg
a single crisis), at the other there are links, and sets of links, which
are considered stable over centuries (eg between the more permanent
(vii) Intensity: A measure of the strength of the link or bond
between two entities. Two problems may be said to be "strongly bound
together". In some cases, the intensity is a measure of the amount
of the "flow" or "transaction" between the entities.
The link from A to B may be strong, and that from B to A, weak.
(viii) Frequency: A link between two entities may only be established
(ix) Rearrangeability and blocking: A connecting network is
an arrangement of entitites and relationships allowing a certain set of
entities to be connected together in various possible combinations. Two
suggestive properties of such networks, which are extensively analyzed
in telephone communications, are: (a) rearrangeability (a networkis rearrangeable,
if alternative paths can be found to link any pair of entities by rearranging
the links between other entities); (b) blocking (a network is in a blocking
state if some pair of entities cannot be connected).
: In considering
the possibility of analyzing networks of problems (organizations, concepts,
), it is important to benefit as much as possible from related
work on artificial intelligence, and possibly pattern recognition. Artificial
intelligence projects to simulate human personality or belief systems have
had to develop mathematical techniques and computer programmes which can
handle and interrelate entitites such as concepts and propositions, some
of which may be positively or negatively loaded to represent positive values
and perceived problems (the credibility and importance of a belief in a
network, and the intensity with which it is held, may also be indicated).
Clearly the objective of such projects is not achieved once a simple inventory
of entities can be examined, even if it is highly structured in the form
of a thesaurus. Of particular interest is the work on "dialogues"
with such belief systems, some of which are established over a period by
extensive interviews with individuals and others which are specially constructed
to simulate paranoia, for example (see references). Presumably it would
be possible to conduct somewhat similar dialogues with the collective beliefs
constituted by problem/value netwroks such as might be developed during
the course of this project.
Despite the available techniques noted above, and others
which have been applied to non-social networks, much would seem to remain
to be accomplished, as François Lorrain's (1) remarks indicated,
in order to grasp networks in their totality.
The question is what it would be useful to know about networks at this
time. What indicators would it be useful to attach to individual problems
) to indicate the characteristics of their relationship
to the network(s) in which they are embedded? What similar indicators would
be useful in describing the relationships between relatively dense networks
and the larger network in which they themselves are embedded? What sort
of concept about networks need to be embodied in a network vocabulary
so that such matters can be discussed intelligently and unambiguously in
public debate? In other words, what are the elements of an adequate vocabulary
of structure and in what disciplines has the basis for such a vocabulary
already been established: chemistry, crystallography, architecture, design
in general, etc
? What can be learnt from biologists about the growth
and development of the many reticular structures they encounter (eg
radiolaria)? More interesting perhaps, in which occupations do some individuals
develop a special (instinctive or intuitive) sensitivity to the structural
and dynamic characteristics of the networks with which, or within which,
they work: airline pilots, urban bus drivers, electricity grid controllers,
counter-espionage directors, factory process controllers, computer-based
data network designer/controllers, telephone exchange designer/ controllers,
institutional fund controllers, etc
? What do such people say, or
want to say, about their networks? Why has the term "networking"
suddenly sprung into common use and consequently what could "to network"
mean? It is questionable whether any adequate organizational response (a
) to the world problem complex can be elaborated
until such rich experience is collected together and matched to an elaborated,
mathematically-based concept structure, and an associated vocabulary. A
conceptual quantum jump is required to grasp problem (and other organized)
structures in their totality and be able to communicate such insights.
It is hoped that the availability of the data in this publication will
help to stimulate such fresh thinking on the conceptual containment of