From ecfe7cbed6f9fa3267ecbc5eefeaecb4a68c89f8 Mon Sep 17 00:00:00 2001
From: Mart Lubbers <mart@martlubbers.net>
Date: Tue, 18 Nov 2014 09:39:55 +0100
Subject: [PATCH] small add

---
 thesis2/1.introduction.tex | 22 ++++++++++++++---
 thesis2/thesis.blg         | 49 ++++++++++++++++++++++++++++++++++++++
 2 files changed, 68 insertions(+), 3 deletions(-)
 create mode 100644 thesis2/thesis.blg

diff --git a/thesis2/1.introduction.tex b/thesis2/1.introduction.tex
index c408630..129e38d 100644
--- a/thesis2/1.introduction.tex
+++ b/thesis2/1.introduction.tex
@@ -290,9 +290,25 @@ techniques of recognizing data in text can still be used to interpret the
 isolated extracted parts from this project.
 
 \section{Directed Acyclic Graphs}
-A graph is a mathematical structure described with the ordered pair: $G=(V,E)$.
-In this ordered pair $V$ is the set of nodes and $E$ is set of ordered pairs
-that we will call \textit{undirected edges}.
+A graph($G$) is a mathematical structure to describe relations between nodes
+with edges. A standard graph is defined as the ordered pair: $G=(V,E)$.  In
+this ordered pair $V$ is the set of nodes and $E$ is set of undirected edges
+where every undirected edge is a tuple of two nodes.
+Figure~\ref{fig:graphexample} is specified as: 
+	$$G=({n1, n2, n3}, {(n1, n2), (n2, n3), (n2, n3)})$$
+
+\begin{figure}[H]
+	\caption{Example Graph}
+	\label{fig:graphexample}
+	\centering
+	\digraph[]{graphexample}{
+		rankdir=LR
+		n1 -> n2 [dir="none"]
+		n2 -> n3 [dir="none"]
+		n2 -> n3 [dir="none"]
+	}
+\end{figure}
+
 
 Directed graphs are special kinds of graphs. A directed graph is described as
 the ordered pair: $G=(V,A)$. Where $A$ is a set of ordered pairs that we will
diff --git a/thesis2/thesis.blg b/thesis2/thesis.blg
new file mode 100644
index 0000000..5fd3b2d
--- /dev/null
+++ b/thesis2/thesis.blg
@@ -0,0 +1,49 @@
+This is BibTeX, Version 0.99d (TeX Live 2015/dev/Debian)
+Capacity: max_strings=35307, hash_size=35307, hash_prime=30011
+The top-level auxiliary file: thesis.aux
+The style file: plain.bst
+Database file #1: thesis.bib
+Warning--empty institution in Hopcroft1971
+Warning--empty journal in Roelofs2008
+You've used 4 entries,
+            2118 wiz_defined-function locations,
+            521 strings with 4555 characters,
+and the built_in function-call counts, 1196 in all, are:
+= -- 114
+> -- 55
+< -- 1
++ -- 22
+- -- 18
+* -- 78
+:= -- 211
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+empty$ -- 92
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+text.length$ -- 1
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+top$ -- 0
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+warning$ -- 2
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+width$ -- 5
+write$ -- 43
+(There were 2 warnings)
-- 
2.20.1