Biology Reference
In-Depth Information
The topological ordering induced by the graph structure is
(
{
F
,
G
,
H
},{
C
,
B
},{
A
},{
D
,
E
},{
L
,
K
}
)
.
(1.1)
The nodes are only
partially ordered
; for example, no ordering can be established
among root nodes or leaf nodes. As a result, in practice the topological ordering of a
directed acyclic graph is defined over a set of unordered sets of nodes, denoted with
V
i
=
{
v
i
1
,...,
v
i
k
}
, defining a partition of
V
.
1.1.3 Further Reading
For a broader coverage of the properties of directed and mixed graphs, we refer the
reader to the monograph by
Bang-Jensen and Gutin
(
2009
), which at the time of
this writing is the most complete reference on the subject. For undirected graphs,
we refer to the classic topic of
Diestel
(
2005
).
1.2 The
R
Environment for Statistical Computing
R
(
R Development Core Team
,
2012
) is a programming language and an environ-
ment targeted at statistical computing, released as an open-source software under the
R
supports all common operating systems (Windows, MacOS X and Linux) in
addition to several Unix variants and has been constantly updated and improved
over the years to become a standard choice for data analysis and the development of
new statistical techniques.
1.2.1 Base Distribution and Contributed Packages
The
R
environment consists of a
base distribution
, maintained and developed by
the
R
Core Team, and a constantly growing set of
contributed packages
.Bothare
distributed through a network of servers called “The Comprehensive R Archive Net-
work” (CRAN), which provides up-to-date mirrors of the main site, located at
http://
The base distribution provides a set of standard packages implementing the basic
functionality of
R
, including the following:
•
Probability, density, distribution, and quantile functions for commonly used prob-
ability distributions
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