I presume you are trying to install that package using sudo dpkg -i package, well, that normally leads to package dependency problems so normally I suggest the use of gdebi. If you have any problematic package remove it. You can check using sudo apt-get check. Now down to business:

sudo apt-get install gdebi-core

With that we have ready gdebi. Now if you use a 64-bit system you may like to install the 64-bit package, likewise with 32-bits. If you use 32-bits:

wget http://www.graphviz.org/pub/graphviz/stable/ubuntu/ub13.10/i386/graphviz_2.36.0-1~saucy_i386.deb

If you use 64-bits:

wget http://www.graphviz.org/pub/graphviz/stable/ubuntu/ub13.10/x86_64/graphviz_2.36.0-1~saucy_amd64.deb

Now here comes the funny stuff...

sudo gdebi graphviz_2.37.20140208.0545-1\~saucy_amd64.deb 
Reading package lists... Done
Building dependency tree        
Reading state information... Done
Building data structures... Done 
Building data structures... Done 
This package is uninstallable
Dependency is not satisfiable: libgd2-noxpm (>= 2.0.36~rc1~dfsg)|libgd2-xpm (>= 2.0.36~rc1~dfsg)

And here is where you stop. The reason is that the stable package depends on package that were dropped of Debian, ergo Ubuntu 13.10:

libgd2 (2.0.36~rc1~dfsg-6.1) unstable; urgency=low

  * Non-maintainer upload.
  * Support multi-arch: (closes: #652496)
    - Mark libgd2-xpm, libgd2-noxpm, libgd2-xpm-dev and libgd2-noxpm-dev
      as same.
    - Adjust d-shlibs and dh-buildinfo build-dependency.
  * Drop .la files.

 -- Bastian Blank   Sun, 13 May 2012 09:16:37 +0000

Those are dependencies of graphviz so they should change them to libgd2-xpm-dev and libgd2-noxpm-dev respectively. The problem is that this is not easy to report in the bugtracker since it's a trivial change. So... lets hack it!

The hack

There are two ways, you can uncompress the deb file look for the dependency and modify it by hand or get the sources and built it yourself. Is up to you. You need to extract the DEBIAN/control file and then run the following:

sed -i 's/libgd2-xpm/libgd2-xpm-dev/g' control
sed -i 's/libgd2-noxpm/libgd2-noxpm-dev/g' control

Pack the file again and done.

I presume you are trying to install that package using sudo dpkg -i package, well, that normally leads to package dependency problems so normally I suggest the use of gdebi. If you have any problematic package remove it. You can check using sudo apt-get check. Now down to business:

sudo apt-get install gdebi-core

With that we have ready gdebi. Now if you use a 64-bit system you may like to install the 64-bit package, likewise with 32-bits.

Now here comes the funny stuff...

sudo gdebi graphviz_2.37.20140208.0545-1\~saucy_amd64.deb 
Reading package lists... Done
Building dependency tree        
Reading state information... Done
Building data structures... Done 
Building data structures... Done 
This package is uninstallable
Dependency is not satisfiable: libgd2-noxpm (>= 2.0.36~rc1~dfsg)|libgd2-xpm (>= 2.0.36~rc1~dfsg)

And here is where you stop. The reason is that the stable package depends on package that were dropped of Debian, ergo Ubuntu 13.10:

libgd2 (2.0.36~rc1~dfsg-6.1) unstable; urgency=low

  * Non-maintainer upload.
  * Support multi-arch: (closes: #652496)
    - Mark libgd2-xpm, libgd2-noxpm, libgd2-xpm-dev and libgd2-noxpm-dev
      as same.
    - Adjust d-shlibs and dh-buildinfo build-dependency.
  * Drop .la files.

 -- Bastian Blank   Sun, 13 May 2012 09:16:37 +0000

Those are dependencies of graphviz so they should change them to libgd2-xpm-dev and libgd2-noxpm-dev respectively. If that's the case, you should download the latest build instead 2.38 or later, which includes the correct dependencies.