From: asutton_at_[hidden]
Date: 2007-08-15 10:36:01
Author: asutton
Date: 2007-08-15 10:36:00 EDT (Wed, 15 Aug 2007)
New Revision: 38680
URL: http://svn.boost.org/trac/boost/changeset/38680
Log:
Adding eqs for betweenness and related measures.
Removing total geodesic (farness) and inverse geodesic (norm close)
Added:
sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/betweenness.tex (contents, props changed)
sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/central_point_dominance.tex (contents, props changed)
sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/relative_betweenness.tex (contents, props changed)
Removed:
sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/inverse_geodesic.tex
sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/total_geodesic.tex
Text files modified:
sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/Makefile | 7 ++++---
sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/graph_mean_geodesic.tex | 8 ++++----
sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/mean_geodesic.tex | 2 +-
3 files changed, 9 insertions(+), 8 deletions(-)
Modified: sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/Makefile
==============================================================================
--- sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/Makefile (original)
+++ sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/Makefile 2007-08-15 10:36:00 EDT (Wed, 15 Aug 2007)
@@ -1,11 +1,12 @@
src = \
- total_geodesic.tex \
mean_geodesic.tex \
graph_mean_geodesic.tex \
- inverse_geodesic.tex \
closeness.tex \
- norm_closeness.tex
+ norm_closeness.tex \
+ betweenness.tex \
+ relative_betweenness.tex \
+ central_point_dominance.tex
dvi = $(src:%.tex=%.dvi)
ps = $(src:%.tex=%.ps)
png = $(src:%.tex=%.png)
Added: sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/betweenness.tex
==============================================================================
--- (empty file)
+++ sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/betweenness.tex 2007-08-15 10:36:00 EDT (Wed, 15 Aug 2007)
@@ -0,0 +1,15 @@
+\documentclass[12pt]{article}
+
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{pst-plot}
+\usepackage{color}
+\pagestyle{empty}
+
+\begin{document}
+\[
+C_B\left(v\right) = \sum_{s \neq v \neq t \in V}
+ \frac{\delta_{st}\left(v\right)}{\delta_{st}}
+\]
+\end{document}
\ No newline at end of file
Added: sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/central_point_dominance.tex
==============================================================================
--- (empty file)
+++ sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/central_point_dominance.tex 2007-08-15 10:36:00 EDT (Wed, 15 Aug 2007)
@@ -0,0 +1,16 @@
+\documentclass[12pt]{article}
+
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{pst-plot}
+\usepackage{color}
+\pagestyle{empty}
+
+\begin{document}
+\[
+C'_B\left(G\right) = \frac
+ {\sum_{v \in V}{C_B\left(v^{*}\right) - C'_B\left(v\right)}}
+ {n - 1}
+\]
+\end{document}
\ No newline at end of file
Modified: sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/graph_mean_geodesic.tex
==============================================================================
--- sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/graph_mean_geodesic.tex (original)
+++ sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/graph_mean_geodesic.tex 2007-08-15 10:36:00 EDT (Wed, 15 Aug 2007)
@@ -11,10 +11,10 @@
\[
\bar{D}\left(G\right)
= \frac
- {2\displaystyle\sum_{u \in V}{\bar{D}\left(u\right)}}
- {\left(\left|V\right|+1\right)}
+ {\displaystyle\sum_{u \in V}{\bar{D}\left(u\right)}}
+ {\left(\left|V\right|\right)}
= \frac
- {2\displaystyle\sum_{u \in V}\sum_{v \in V}{d\left(u,v\right)}}
- {\left|V\right| \cdot \left(\left|V\right|+1\right)}
+ {\displaystyle\sum_{u \in V}\sum_{v \in V}{d\left(u,v\right)}}
+ {\left|V\right| \cdot \left(\left|V\right|-1\right)}
\]
\end{document}
\ No newline at end of file
Deleted: sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/inverse_geodesic.tex
==============================================================================
--- sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/inverse_geodesic.tex 2007-08-15 10:36:00 EDT (Wed, 15 Aug 2007)
+++ (empty file)
@@ -1,15 +0,0 @@
-\documentclass[12pt]{article}
-
-\usepackage{amsmath}
-\usepackage{amsfonts}
-\usepackage{amssymb}
-\usepackage{pst-plot}
-\usepackage{color}
-\pagestyle{empty}
-
-\begin{document}
-\[
-\bar{D}^{-1}\left(u\right) =
- \frac{\left|V\right|}{\sum_{v \in V}{d\left(u,v\right)}}
-\]
-\end{document}
\ No newline at end of file
Modified: sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/mean_geodesic.tex
==============================================================================
--- sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/mean_geodesic.tex (original)
+++ sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/mean_geodesic.tex 2007-08-15 10:36:00 EDT (Wed, 15 Aug 2007)
@@ -10,6 +10,6 @@
\begin{document}
\[
\bar{D}\left(u\right) =
- \frac{\sum_{v \in V}{d\left(u,v\right)}}{\left|V\right|}
+ \frac{\sum_{v \in V}{d\left(u,v\right)}}{\left|V\right|-1}
\]
\end{document}
\ No newline at end of file
Added: sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/relative_betweenness.tex
==============================================================================
--- (empty file)
+++ sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/relative_betweenness.tex 2007-08-15 10:36:00 EDT (Wed, 15 Aug 2007)
@@ -0,0 +1,16 @@
+\documentclass[12pt]{article}
+
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{pst-plot}
+\usepackage{color}
+\pagestyle{empty}
+
+\begin{document}
+\[
+C'_B\left(v\right) = C_B\left(v\right)\frac{2}{\left(n - 1\right)\left(n - 2\right)}
+=
+C_B\left(v\right)\frac{2}{n^2-3n+2}
+\]
+\end{document}
\ No newline at end of file
Deleted: sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/total_geodesic.tex
==============================================================================
--- sandbox/SOC/2007/graphs/libs/graph/doc/images/eq/total_geodesic.tex 2007-08-15 10:36:00 EDT (Wed, 15 Aug 2007)
+++ (empty file)
@@ -1,14 +0,0 @@
-\documentclass[12pt]{article}
-
-\usepackage{amsmath}
-\usepackage{amsfonts}
-\usepackage{amssymb}
-\usepackage{pst-plot}
-\usepackage{color}
-\pagestyle{empty}
-
-\begin{document}
-\[
-D\left(u\right) = \sum_{v \in V}{d\left(u,v\right)}
-\]
-\end{document}d_G\left(u,v\right)
\ No newline at end of file