# Cluster diagrams

**Diagrams** are sometimes known as *graphs*.

## Chain clusters[edit]

A *chain* is a cluster with at least one node.
All routes from one base point to the other pass through at least one nodal
field point. Cutting at this point separates the diagram into two parts,
each of which contains a base point. A *simple chain* is one in which
every field point is a node. A *netted chain* is one that can
be formed from a simple chain by adding not more than one field point
across each link of the simple chain.

## Bundles[edit]

A *bundle* is a parallel collection of links.
It has no nodes since there is always more than one independent path
from one base point to the other.

## Elementary Clusters[edit]

An *elementary* cluster is that which is neither a chain or a bundle.

where *C(r)* is the set of *chain* clusters, *B(r)* is the set of *bundles*, and
*E(r)* is the set of *elementary* clusters (Eq. 5.2 Ref. 1).
Similarly,

## Lemmas[edit]

There are five lemmas (see Ref.s 2,3 and 4).

## See also[edit]

## References[edit]

- J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics
*28'*pp. 169-199 (1965) - Tohru Morita and Kazuo Hiroike "A New Approach to the Theory of Classical Fluids. III General Treatment of Classical Systems", Progress of Theoretical Physics
**25**pp. 537-578 (1961) - Cyrano De Dominicis "Variational Formulations of Equilibrium Statistical Mechanics", Journal of Mathematical Physics
**3**pp. 983-1002 (1962) - Cyrano De Dominicis "Variational Statistical Mechanics in Terms of "Observables" for Normal and Superfluid Systems", Journal of Mathematical Physics
**4**pp. 255-265 (1963)