Here are some steps you can take to alleviate this problem. You can combine them as you wish to meet your needs:
- Reduce the margins. You are already using
geometry to set your margins to 1 inch. You can reduce this for all the margins using the margin key you're already using, but geometry also provides keys for setting the horizontal and vertical margins separately (e.g., \usepackage[vmargin=1in, hmargin=0.75in]{geometry}.
- Eliminate the indent before the example number. Put
\exewidth{(\thexnumi)} in your preamble. (See this answer by Alan Munn).
- Hyphenate long words. You can simply add another line to your
deptext environment and split long words onto two lines (see section 3 of the tikz-dependency documentation, as well as my example below). You can add as many lines as you'd like.
- Reduce the font size. To change the size of the nodes but not the size of the labels on the arrows, pass the
font option to the deptext environment. For example, \begin{deptext}[font=\scriptsize] will make the node text scriptsize but keep the label text the same as before.
- Scale the graph down. This will reduce the font size of all the text, including labels, as well as reduce the size of the arrows. For example, use
\scalebox{0.7}{\begin{dependency}...\end{dependency}} to scale the whole graph down by 30%, keeping the original proportions. This is a graphicx command; graphicx is loaded by tikz, which is loaded by tikz-dependency, so you don't need to add anything to your preamble to use this.
Example 1
In the example below, I've eliminated the indentation before the example number and hyphenated some of the longer words (following the morpheme boundaries in your glosses). I've added the showframe package to show that this makes the graph fit within the 1-inch margins you had specified.
\documentclass[12pt]{article}
\usepackage[margin=1in]{geometry}
\setlength\parindent{0.25in}
\bibliographystyle{chicago}
\usepackage{natbib}
\usepackage[english]{babel}
\newcommand{\itab}[1]{\hspace{0em}\rlap{#1}}
\newcommand{\tab}[1]{\hspace{.2\textwidth}\rlap{#1}}
\usepackage{setspace}
\usepackage{graphicx}
\usepackage{indentfirst}
\usepackage{hyperref}
\usepackage{tikz-dependency}
\usepackage{gb4e}
\exewidth{(\thexnumi)} % as suggested by Alan Munn at http://permalink.gmane.org/gmane.comp.tex.linguistics/1610
\usepackage{showframe} % used to show margin lines
\begin{document}
\begin{exe}
\ex{Con20.019 - Parallel roots and shared arguments}\\
\begin{dependency}[theme = simple]
\begin{deptext}
Nehe' \& nebesiiwoho' \& nihP \& how3o'- \& nono'eiP \& hih'oow- \& nihbeexo'u-\\
\& \& \& uuni \& \& nih'oo3ouyeitino', \& unono'eitisi3i'. \\
\end{deptext}
\depedge{1}{2}{\textsc{det}}
\depedge{2}{6}{\textsc{sbjct.pp}}
\depedge[arc angle = 20, edge below]{2}{7}{\textsc{agent.pp}}
\depedge{3}{6}{\textsc{repr}}
\depedge{4}{6}{\textsc{skip}}
\depedge{5}{6}{\textsc{repr}}
\deproot{6}{\textsc{root}}
\depedge{7}{6}{\textsc{rootp}}
\end{dependency}
\glll
nehe' ne-besiiwoho' nih-P how3o'-uuni {nono'eiti-P} {hih'oow-nih'oo3ouyeiti-no’} {nih-beexo'u-unono'eitis-i3i’}\\
this 1S-grandfathers PAST-pause/break never-DETACH {speak Arapaho-pause/break} {3.PAST.NEG-speak English-pers.PL} {PAST-only-speak Arapaho to-3PL/1S}\\
det infl-na.oblposs.pl prefix-P prefix-deriv {vai-P} {infl+prefix-vai.incorp-infl} {prefix-prefix-vta.incorp.1S-infl}\\
\trans ``My grandfathers never spoke English, they only spoke Arapaho to me.''
\end{exe}
\end{document}
Example 2
In this example, I've reduced the horizontal margins to 0.75 inches and reduced the size of the node text to footnotesize.
\documentclass[12pt]{article}
\usepackage[vmargin=1in, hmargin=0.75in]{geometry}
\setlength\parindent{0.25in}
\bibliographystyle{chicago}
\usepackage{natbib}
\usepackage[english]{babel}
\newcommand{\itab}[1]{\hspace{0em}\rlap{#1}}
\newcommand{\tab}[1]{\hspace{.2\textwidth}\rlap{#1}}
\usepackage{setspace}
\usepackage{graphicx}
\usepackage{indentfirst}
\usepackage{hyperref}
\usepackage{tikz-dependency}
\usepackage{gb4e}
\usepackage{showframe} % used to show margin lines
\begin{document}
\begin{exe}
\ex{Con20.019 - Parallel roots and shared arguments}\\
\begin{dependency}[theme = simple]
\begin{deptext}[font=\footnotesize]
Nehe' \& nebesiiwoho' \& nihP \& how3o'uuni \& nono'eiP \& hih'oownih'oo3ouyeitino', \& nihbeexo'uunono'eitisi3i'.\\
\end{deptext}
\depedge{1}{2}{\textsc{det}}
\depedge{2}{6}{\textsc{sbjct.pp}}
\depedge[arc angle = 20, edge below]{2}{7}{\textsc{agent.pp}}
\depedge{3}{6}{\textsc{repr}}
\depedge{4}{6}{\textsc{skip}}
\depedge{5}{6}{\textsc{repr}}
\deproot{6}{\textsc{root}}
\depedge{7}{6}{\textsc{rootp}}
\end{dependency}
\glll
nehe' ne-besiiwoho' nih-P how3o'-uuni {nono'eiti-P} {hih'oow-nih'oo3ouyeiti-no’} {nih-beexo'u-unono'eitis-i3i’}\\
this 1S-grandfathers PAST-pause/break never-DETACH {speak Arapaho-pause/break} {3.PAST.NEG-speak English-pers.PL} {PAST-only-speak Arapaho to-3PL/1S}\\
det infl-na.oblposs.pl prefix-P prefix-deriv {vai-P} {infl+prefix-vai.incorp-infl} {prefix-prefix-vta.incorp.1S-infl}\\
\trans ``My grandfathers never spoke English, they only spoke Arapaho to me.''
\end{exe}
\end{document}
