How to draw clusters with tikz?

Question

I am trying to recreate the cluster diagrams shown below for my homeowrk. Help?

Answer 1

I have finished the job only as exercise after many attemps. Surely it is not a "clean" and "easy" code and it is not the same to 100%. But I have tried to give you an answer. An advice: the next question put a minimal working example! :-). PS: It is not made with tikz: sorry.

\documentclass[a4paper,12pt]{article}
\usepackage{geometry}
\usepackage{newtxtext,newtxmath}
\usepackage{amssymb,stackengine}
\usepackage{graphicx}
\usepackage[all]{xy}
\usepackage{parskip}
\begin{document}
[\underset{1}{\bullet}\qquad \xymatrix@R=.2pt@C=.2pt{
\underset{2}{\bullet} \ar@{-}[rr] & & \underset{3}{\bullet}}\qquad \xymatrix@R=.2pt@C=.2pt{
\underset{4}{\bullet} \ar@{-}[rr] & &\underset{5}{\bullet} \ar@{-}[rr]& & \underset{6}{\bullet}}\quad \cdots \underset{N}{\bullet}]
[b_2=\resizebox{25pt}{!}{\stackon[-2pt]{}{\xymatrix@R=.2pt@C=.2pt{
{ \bullet} \ar@{-}[rr] & & {\bullet}}}}=
\int d^3\vec{q}_1\cdots\text{you could to continue to complete it.}]
There are four diagrams contibuiting to $b_3$, leading to
[b_3=\resizebox{25pt}{!}{\stackon[-4pt]{}{\xymatrix@R=.2pt@C=.2pt{
& {\bullet} \ar@{-}[ldd] & \
&  & \
{\bullet} \ar@{-}[rr]&  &{\bullet} }}} \quad +\quad \resizebox{25pt}{!}{\stackon[-4pt]{}{
\xymatrix@R=.2pt@C=.2pt{
& {\bullet} \ar@{-}[rdd] & \
&  & \
{\bullet} \ar@{-}[rr]&  &{\bullet} }}}\quad +\quad \resizebox{25pt}{!}{\stackon[-4pt]{}{
\xymatrix@R=.2pt@C=.2pt{
& {\bullet} \ar@{-}[ldd]\ar@{-}[rdd] & \
&  & \
{\bullet} &  &{\bullet} }}}\quad +\quad \resizebox{25pt}{!}{\stackon[-4pt]{}{
\xymatrix@R=.2pt@C=.2pt{
& {\bullet} \ar@{-}[ldd]\ar@{-}[rdd] & \
&  & \
{\bullet} \ar@{-}[rr]&  &{\bullet} }}}
]
[=\int d^3\vec{q}_1\cdots\text{you could to continue to complete it.}]
\end{document}