Is it possible to use tikz in notebook

edit

As long as you have tikz installed in your TeX installation, then sure, you can use tikz. See Sage's tutorial for information about how to tell Sage to use LaTeX to produce pictures in the notebook rather than jsMath or MathJax (these are the default, jsMath in older versions of Sage, MathJax in the most recent). Briefly:

from sage.graphs.graph_latex import setup_latex_preamble
setup_latex_preamble()
latex.add_to_jsmath_avoid_list('tikz')
view(g)

should do it. Read the referenced section of the tutorial and also the following section.

Edit: using your vertex labels, I get a LaTeX error when I try this. So I modified your graph like this:

h1 = r"$\text{House 1}$"
h2 = r"$\text{House 2}$"
h3 = r"$\text{House 3}$"
w = r"$\text{Water}$"
e = r"$\text{Electricity}$"
ph = r"$\text{Phone Line}$"
f = {h1: [w, e, ph], h2: [w, e, ph], h3: [w, e]}
g = Graph(f)
from sage.graphs.graph_latex import setup_latex_preamble
setup_latex_preamble()
latex.extra_preamble()
latex.add_to_mathjax_avoid_list('tikz')
latex.engine('pdflatex')
view(g)

Unfortunately, with these vertex labels, g.plot(...) doesn't work anymore. There may be ways of tinkering with the graph to get both view (using LaTeX) and plot to work.

No, you need a full installation of TeX for this. While mathjax (the engine to render TeX in sage nb) is quite capable, it can't do tikz.