From 4260c1ffbf9b55e7e5b0540aba35548b1a9ba8b8 Mon Sep 17 00:00:00 2001 From: Tristan-Raz Date: Thu, 15 May 2025 12:17:58 -0400 Subject: [PATCH 1/8] added a label and xml: id to the exercises issue#248 --- .../ComplexityScience/DifferentModelsForDifferentPurposes.ptx | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/pretext/ComplexityScience/DifferentModelsForDifferentPurposes.ptx b/pretext/ComplexityScience/DifferentModelsForDifferentPurposes.ptx index 1a6065b..bb4b971 100755 --- a/pretext/ComplexityScience/DifferentModelsForDifferentPurposes.ptx +++ b/pretext/ComplexityScience/DifferentModelsForDifferentPurposes.ptx @@ -15,7 +15,7 @@

Reductionism is the view that the behavior of a system can be explained by understanding its components. For example, the periodic table of the elements is a triumph of reductionism, because it explains the chemical behavior of elements with a model of electrons in atoms. Holism is the view that some phenomena that appear at the system level do not exist at the level of components, and cannot be explained in component-level terms.

We get back to explanatory models in , instrumentalism in , and holism in

- +

Q-1: Classical models are better to

@@ -39,7 +39,7 @@ - +

Q-2: Complex Models are better to

From b550c48f193eef6ed380e9e0693f9c7e04d5424b Mon Sep 17 00:00:00 2001 From: Tristan-Raz Date: Thu, 15 May 2025 12:42:01 -0400 Subject: [PATCH 2/8] Added alt tags to the images to help explain fixes issue #254 --- pretext/AlgorithmAnalysis/BigONotation.ptx | 4 ++-- pretext/AlgorithmAnalysis/WhatIsAlgorithmAnalysis.ptx | 2 +- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/pretext/AlgorithmAnalysis/BigONotation.ptx b/pretext/AlgorithmAnalysis/BigONotation.ptx index 8fb0afc..067f1a5 100755 --- a/pretext/AlgorithmAnalysis/BigONotation.ptx +++ b/pretext/AlgorithmAnalysis/BigONotation.ptx @@ -199,7 +199,7 @@ another.

Figure 1: Common Big-O Functions - + Graph of common Big-O functions (constant, logarithmic, linear, n log n, quadratic, cubic, exponential) showing their comparative growth rates as n increases.
@@ -252,7 +252,7 @@ main() ignored as n grows larger.

Figure 2: Comparing T(n) with Big-O Functions - + Graph comparing a specific T(n) function (3n^2+2n+4) with Big-O functions like O(n^2) and O(n^3), illustrating how T(n) follows the O(n^2) curve as n increases.

shows a few of the common Big-O functions as they compare with the T(n) function discussed above. Note that diff --git a/pretext/AlgorithmAnalysis/WhatIsAlgorithmAnalysis.ptx b/pretext/AlgorithmAnalysis/WhatIsAlgorithmAnalysis.ptx index d05e590..4ead1b2 100755 --- a/pretext/AlgorithmAnalysis/WhatIsAlgorithmAnalysis.ptx +++ b/pretext/AlgorithmAnalysis/WhatIsAlgorithmAnalysis.ptx @@ -237,7 +237,7 @@ main() following 8 \times 9.rectangle.

Figure 1: Sum of n = 8 integers - + Diagram illustrating the sum of the first 8 integers as a blue area within an 8x9 rectangle. The blue area represents 1+2+3+4+5+6+7+8 squares.

To find the blue area, we can count the number of blue squares 1+2+3+4+5+6+7+8, which we just learned From c86aa60380e54d686df5af33da66bb56f4d42467 Mon Sep 17 00:00:00 2001 From: Tristan-Raz Date: Thu, 15 May 2025 18:09:53 -0400 Subject: [PATCH 3/8] Added much more descriptive lanugage and fixes issue #247 --- pretext/Graphs/Generating.ptx | 2 +- pretext/Graphs/GeneratingER.ptx | 2 +- pretext/Graphs/NetworkX.ptx | 2 +- pretext/Graphs/ProbabilityOfConnectivity.ptx | 4 ++-- 4 files changed, 5 insertions(+), 5 deletions(-) diff --git a/pretext/Graphs/Generating.ptx b/pretext/Graphs/Generating.ptx index ddb7d21..49d1725 100755 --- a/pretext/Graphs/Generating.ptx +++ b/pretext/Graphs/Generating.ptx @@ -3,7 +3,7 @@ Generating Graphs

A complete graph with 10 nodes. - " A complete graph with 10 nodes." + "Ten circular nodes, labeled 0 to 9, are arranged in a circular pattern. A dense mesh of straight edges connects every node to all other nodes, visually representing a complete graph."

We'll start by generating a complete graph, which is a graph where every node is connected to every other.

Here's a generator function that takes a list of nodes and enumerates all distinct pairs. If you are not familiar with generator functions.

diff --git a/pretext/Graphs/GeneratingER.ptx b/pretext/Graphs/GeneratingER.ptx index 8c9d68e..98fc503 100755 --- a/pretext/Graphs/GeneratingER.ptx +++ b/pretext/Graphs/GeneratingER.ptx @@ -3,7 +3,7 @@ Generating ER Graphs
An ER graph with n=10 and p=0.3. - " An ER graph with n=10 and p=0.3." + " An Erdős-Rényi (ER) random graph with 10 circular nodes, labeled 0 to 9, displayed in a somewhat irregular layout. Edges connect various pairs of nodes, but not all possible pairs, resulting in a network sparser than a complete graph. For instance, node 3 connects only to node 2, while other nodes like 7 have multiple connections."

The ER graph G(n, p) contains n nodes, and each pair of nodes is connected by an edge with probability p. Generating an ER graph is similar to generating a complete graph.

The following generator function enumerates all possible edges and chooses which ones should be added to the graph:

diff --git a/pretext/Graphs/NetworkX.ptx b/pretext/Graphs/NetworkX.ptx index ed13ba2..9eef86e 100755 --- a/pretext/Graphs/NetworkX.ptx +++ b/pretext/Graphs/NetworkX.ptx @@ -3,7 +3,7 @@ NetworkX
An undirected graph that represents driving time between cities. - " An undirected graph that represents driving time between cities." + " Undirected graph with four square nodes labeled Albany, Boston, NYC, and Philly, arranged to approximate their geographical locations. Edges connect specific city pairs and are labeled with driving times: Albany-Boston (3 hrs), Albany-NYC (4 hrs), Boston-NYC (4 hrs), and NYC-Philly (2 hrs)."

To represent graphs, we'll use a package called NetworkX, which is the most commonly used network library in Python.

We can create a directed graph by importing NetworkX (usually imported as nx) and instantiating nx.DiGraph:

diff --git a/pretext/Graphs/ProbabilityOfConnectivity.ptx b/pretext/Graphs/ProbabilityOfConnectivity.ptx index 2764c6c..56f070f 100755 --- a/pretext/Graphs/ProbabilityOfConnectivity.ptx +++ b/pretext/Graphs/ProbabilityOfConnectivity.ptx @@ -3,11 +3,11 @@ Probability of Connectivity
Probability of connectivity with n=10 and a range of p. The vertical line shows the predicted critical value. - " Probability of connectivity with n=10 and a range of p. The vertical line shows the predicted critical value" + " Line graph showing the probability of graph connectivity for n=10 as the probability of an edge (p) varies. The x-axis (log scale) represents 'Prob of edge (p)' from 10^-2.5 to 1. The y-axis represents 'Prob connected' from 0.0 to 1.0. A blue S-shaped curve rises from near 0 to near 1, with the steepest ascent around p=0.23, where a vertical gray line indicates the predicted critical value."
Probability of connectivity for several values of n and a range of p. - " Probability of connectivity for several values of n and a range of p." + "Line graph comparing probability of graph connectivity for different numbers of nodes (n) as the probability of an edge (p) varies. The x-axis (log scale) is 'Prob of edge (p)' from 10^-2.5 to 1. The y-axis is 'Prob connected' from 0.0 to 1.0. Three S-shaped curves are shown: for n=30 (dark blue), n=100 (medium blue), and n=300 (light blue). As n increases, the S-curve shifts to the left and its transition becomes more abrupt. Each curve has a faint vertical line indicating its critical point."

For given values of n and p, we would like to know the probability that G(n, p) is connected. We can estimate it by generating a large number of random graphs and counting how many are connected. Here's how:

def prob_connected(n, p, iters=100):

From 5d249b3864430954b56c832b80d6207b28217a03 Mon Sep 17 00:00:00 2001
From: Tristan-Raz 
Date: Thu, 15 May 2025 18:49:22 -0400
Subject: [PATCH 4/8] Changed the alt tags back to the regular alt tags and
 added a description and short description for accessibility solves issue #256

---
 pretext/Graphs/GeneratingER.ptx              |  7 ++++++-
 pretext/Graphs/NetworkX.ptx                  | 13 ++++++++++++-
 pretext/Graphs/ProbabilityOfConnectivity.ptx | 18 ++++++++++++++++--
 pretext/Graphs/SelfCheck.ptx                 | 14 +++++++++++++-
 pretext/Graphs/WhatIsAGraph.ptx              | 12 +++++++++++-
 5 files changed, 58 insertions(+), 6 deletions(-)

diff --git a/pretext/Graphs/GeneratingER.ptx b/pretext/Graphs/GeneratingER.ptx
index 98fc503..03ab53f 100755
--- a/pretext/Graphs/GeneratingER.ptx
+++ b/pretext/Graphs/GeneratingER.ptx
@@ -3,7 +3,12 @@
   Generating ER Graphs
   

      An ER graph with n=10 and p=0.3.
-    " An Erdős-Rényi (ER) random graph with 10 circular nodes, labeled 0 to 9, displayed in a somewhat irregular layout. Edges connect various pairs of nodes, but not all possible pairs, resulting in a network sparser than a complete graph. For instance, node 3 connects only to node 2, while other nodes like 7 have multiple connections."
+    " Figure 4.4: An ER graph with n=10 and p=0.3."
+Visual representation of an Erdős-Rényi random graph with 10 nodes and specific edge connections based on p=0.3.
+      
+        
The image displays an Erdős-Rényi (ER) random graph. It features 10 circular nodes, which are labeled with integers from 0 to 9. These nodes are arranged in a somewhat irregular, non-grid layout across the viewing area.

+        
Edges, represented as lines, connect various pairs of these nodes. The graph is not complete, meaning not all possible pairs of nodes are connected. This visual sparsity is characteristic of an ER graph where edges form with a probability p (in this case, p=0.3 for n=10 nodes). For instance, the visual details show that node 3 is connected only to node 2, while other nodes, such as node 7, exhibit multiple connections to different nodes within the graph.

+      
   

   
The ER graph G(n, p) contains n nodes, and each pair of nodes is connected by an edge with probability p. Generating an ER graph is similar to generating a complete graph.

   
The following generator function enumerates all possible edges and chooses which ones should be added to the graph:

diff --git a/pretext/Graphs/NetworkX.ptx b/pretext/Graphs/NetworkX.ptx
index 9eef86e..9e79dd7 100755
--- a/pretext/Graphs/NetworkX.ptx
+++ b/pretext/Graphs/NetworkX.ptx
@@ -3,7 +3,18 @@
   NetworkX
   

      An undirected graph that represents driving time between cities.
-    " Undirected graph with four square nodes labeled Albany, Boston, NYC, and Philly, arranged to approximate their geographical locations. Edges connect specific city pairs and are labeled with driving times: Albany-Boston (3 hrs), Albany-NYC (4 hrs), Boston-NYC (4 hrs), and NYC-Philly (2 hrs)."
+    " Figure 4.2: An undirected graph that represents driving time between cities."
+    Undirected graph showing driving times between Albany, Boston, NYC, and Philly.
+      
+        
The image displays an undirected graph representing a road network with driving times. It features four square-shaped nodes, each labeled with a city name: Albany, Boston, NYC (New York City), and Philly (Philadelphia). These nodes are positioned on the graph to roughly approximate their actual geographical locations relative to each other.

+        
Edges, depicted as lines, connect specific pairs of these cities, indicating direct driving routes. Each edge is labeled with the driving time in hours for that route. The connections and their labeled driving times are as follows:

+        
    
+          
  • Albany to Boston: 3 hours
    • 
+          
  • Albany to NYC: 4 hours
    • 
+          
  • Boston to NYC: 4 hours
    • 
+          
  • NYC to Philly: 2 hours
    • 
+        

+      
   

   
To represent graphs, we'll use a package called NetworkX, which is the most commonly used network library in Python.

   
We can create a directed graph by importing NetworkX (usually imported as nx) and instantiating nx.DiGraph:

diff --git a/pretext/Graphs/ProbabilityOfConnectivity.ptx b/pretext/Graphs/ProbabilityOfConnectivity.ptx
index 56f070f..bfac759 100755
--- a/pretext/Graphs/ProbabilityOfConnectivity.ptx
+++ b/pretext/Graphs/ProbabilityOfConnectivity.ptx
@@ -3,11 +3,25 @@
   Probability of Connectivity
   

      Probability of connectivity with n=10 and a range of p. The vertical line shows the predicted critical value.
-    " Line graph showing the probability of graph connectivity for n=10 as the probability of an edge (p) varies. The x-axis (log scale) represents 'Prob of edge (p)' from 10^-2.5 to 1. The y-axis represents 'Prob connected' from 0.0 to 1.0. A blue S-shaped curve rises from near 0 to near 1, with the steepest ascent around p=0.23, where a vertical gray line indicates the predicted critical value."
+    " Figure 4.5: Probability of connectivity with n=10 and a range of p. The vertical line shows the predicted critical value."
+    Line graph: probability of connectivity (n=10) vs. probability of edge (p).
+      
+        
The graph plots the probability of graph connectivity against the probability of an edge (p) for a graph with n=10 nodes. The x-axis, labeled 'Prob of edge (p)', is on a logarithmic scale ranging from 10^{-2.5} to 10^0=1. The y-axis, labeled 'Prob connected', ranges linearly from 0.0 to 1.0. A blue S-shaped curve illustrates the relationship, showing the probability of connectivity rising from near 0 to near 1. The steepest part of this ascent occurs around p \approx 0.23. A vertical gray line at this x-value indicates the predicted critical value for p.

+      
   

   

      Probability of connectivity for several values of n and a range of p.
-    "Line graph comparing probability of graph connectivity for different numbers of nodes (n) as the probability of an edge (p) varies. The x-axis (log scale) is 'Prob of edge (p)' from 10^-2.5 to 1. The y-axis is 'Prob connected' from 0.0 to 1.0. Three S-shaped curves are shown: for n=30 (dark blue), n=100 (medium blue), and n=300 (light blue). As n increases, the S-curve shifts to the left and its transition becomes more abrupt. Each curve has a faint vertical line indicating its critical point."
+    "Figure 4.6: Probability of connectivity for several values of n and a range of p."
+  Line graph: probability of connectivity vs. probability of edge (p) for n=30, 100, and 300.
+      
+        
This line graph compares the probability of graph connectivity for different numbers of nodes (n) as the probability of an edge (p) varies. The x-axis, labeled 'Prob of edge (p)', is on a logarithmic scale from 10^{-2.5} to 10^0=1. The y-axis, labeled 'Prob connected', ranges from 0.0 to 1.0. Three distinct S-shaped curves are presented:

+        
    
+          
  • A dark blue curve for n=30.
    • 
+          
  • A medium blue curve for n=100.
    • 
+          
  • A light blue curve for n=300.
    • 
+        

+        
The graph illustrates that as the number of nodes (n) increases, the S-shaped curve representing the transition to connectivity shifts to the left (towards lower values of p) and the transition becomes steeper or more abrupt. Each curve is accompanied by a faint vertical line indicating its respective critical point for p.

+      
   

   
For given values of n and p, we would like to know the probability that G(n, p) is connected. We can estimate it by generating a large number of random graphs and counting how many are connected. Here's how:

   
def prob_connected(n, p, iters=100):
diff --git a/pretext/Graphs/SelfCheck.ptx b/pretext/Graphs/SelfCheck.ptx
index ea36347..5039072 100755
--- a/pretext/Graphs/SelfCheck.ptx
+++ b/pretext/Graphs/SelfCheck.ptx
@@ -3,7 +3,19 @@
   Self Check
   

     A Graphical represention of a Friend Network
-    "Graph of Friend Network"
+    " Figure 4.6: Probability of connectivity for several values of n and a range of p."
+      Graph of Friend Network
+    
+        
An undirected graph depicting a social network with five nodes representing individuals: Josh, Kate, Jerry, Mary, and Billy-Bob. Edges connect these individuals as follows:

+        
    
+          
  • Josh is connected to Billy-Bob.
    • 
+          
  • Kate is connected to Jerry, Mary, and Billy-Bob.
    • 
+          
  • Jerry is connected to Kate and Billy-Bob.
    • 
+          
  • Mary is connected to Kate and Billy-Bob.
    • 
+          
  • Billy-Bob is connected to Josh, Kate, Jerry, and Mary, acting as a central connector.
    • 
+        

+        
The connections are mutual, indicating friendships or bidirectional relationships.

+      
   

   
     
diff --git a/pretext/Graphs/WhatIsAGraph.ptx b/pretext/Graphs/WhatIsAGraph.ptx
index 698af8f..22f0ea5 100755
--- a/pretext/Graphs/WhatIsAGraph.ptx
+++ b/pretext/Graphs/WhatIsAGraph.ptx
@@ -3,7 +3,17 @@
   What is a Graph?
   

      A directed graph that represents a social network.
-    " A directed graph that represents a social network."
+    " Figure 4.1: A directed graph that represents a social network. "
+          Directed graph with three nodes illustrating social network connections.
+    
+        
The image displays a simple directed graph consisting of three nodes, visually representing elements in a network. Edges, depicted as arrows, indicate the direction of relationships or flow between these nodes. The specific structure shown is:

+        
    
+          
  • Two of the nodes have a mutual (bidirectional) connection, with arrows pointing from each of these two nodes to the other (Bob and Alice).
    • 
+          
  • Both of these mutually connected nodes also have outgoing arrows pointing towards the third node (Chuck).
    • 
+          
  • The third node (Chuck) is a recipient in these relationships; it only has incoming arrows from the other two nodes and possesses no outgoing arrows.
    • 
+        

+        
This visual structure corresponds to the example given in the text where 'Alice' and 'Bob' follow each other, and both also follow 'Chuck', while 'Chuck' does not follow anyone back.

+      
   

   
To most people a graph is a visual representation of data, like a bar chart or a plot of stock prices over time. That's not what this chapter is about.

   
In this chapter, a graph is a representation of a system that contains discrete, interconnected elements. The elements are represented by nodes — also called vertices – and the interconnections are represented by edges.


From 7619a686f782ff8e649a5705a61741812de0cb96 Mon Sep 17 00:00:00 2001
From: Tristan-Raz 
Date: Thu, 15 May 2025 18:49:55 -0400
Subject: [PATCH 5/8] Changed the alt tags back to the regular alt tags and
 added a description and short description for accessibility solves issue #256

---
 pretext/Graphs/Generating.ptx                | 6 +++++-
 pretext/Graphs/GeneratingER.ptx              | 2 +-
 pretext/Graphs/NetworkX.ptx                  | 2 +-
 pretext/Graphs/ProbabilityOfConnectivity.ptx | 4 ++--
 pretext/Graphs/SelfCheck.ptx                 | 2 +-
 pretext/Graphs/WhatIsAGraph.ptx              | 2 +-
 6 files changed, 11 insertions(+), 7 deletions(-)

diff --git a/pretext/Graphs/Generating.ptx b/pretext/Graphs/Generating.ptx
index 49d1725..fac37a7 100755
--- a/pretext/Graphs/Generating.ptx
+++ b/pretext/Graphs/Generating.ptx
@@ -3,7 +3,11 @@
   Generating Graphs
   

      A complete graph with 10 nodes.
-    "Ten circular nodes, labeled 0 to 9, are arranged in a circular pattern. A dense mesh of straight edges connects every node to all other nodes, visually representing a complete graph."
+    " A complete graph with 10 nodes."
+    Complete graph with 10 nodes.
+      
+        
The image depicts a complete graph consisting of ten nodes. These nodes, labeled 0 through 9, are arranged in a circular pattern for visual clarity. Every node is connected to every other node by a straight edge, forming a dense network where all possible connections are present. This illustrates the fundamental property of a complete graph: full interconnectivity between all its vertices.

+      
   

   
We'll start by generating a complete graph, which is a graph where every node is connected to every other.

   
Here's a generator function that takes a list of nodes and enumerates all distinct pairs. If you are not familiar with generator functions.

diff --git a/pretext/Graphs/GeneratingER.ptx b/pretext/Graphs/GeneratingER.ptx
index 03ab53f..eb3c63c 100755
--- a/pretext/Graphs/GeneratingER.ptx
+++ b/pretext/Graphs/GeneratingER.ptx
@@ -3,7 +3,7 @@
   Generating ER Graphs
   

      An ER graph with n=10 and p=0.3.
-    " Figure 4.4: An ER graph with n=10 and p=0.3."
+    " An ER graph with n=10 and p=0.3."
 Visual representation of an Erdős-Rényi random graph with 10 nodes and specific edge connections based on p=0.3.
       
         
The image displays an Erdős-Rényi (ER) random graph. It features 10 circular nodes, which are labeled with integers from 0 to 9. These nodes are arranged in a somewhat irregular, non-grid layout across the viewing area.

diff --git a/pretext/Graphs/NetworkX.ptx b/pretext/Graphs/NetworkX.ptx
index 9e79dd7..3881f8c 100755
--- a/pretext/Graphs/NetworkX.ptx
+++ b/pretext/Graphs/NetworkX.ptx
@@ -3,7 +3,7 @@
   NetworkX
   

      An undirected graph that represents driving time between cities.
-    " Figure 4.2: An undirected graph that represents driving time between cities."
+    " An undirected graph that represents driving time between cities."
     Undirected graph showing driving times between Albany, Boston, NYC, and Philly.
       
         
The image displays an undirected graph representing a road network with driving times. It features four square-shaped nodes, each labeled with a city name: Albany, Boston, NYC (New York City), and Philly (Philadelphia). These nodes are positioned on the graph to roughly approximate their actual geographical locations relative to each other.

diff --git a/pretext/Graphs/ProbabilityOfConnectivity.ptx b/pretext/Graphs/ProbabilityOfConnectivity.ptx
index bfac759..b8a65d5 100755
--- a/pretext/Graphs/ProbabilityOfConnectivity.ptx
+++ b/pretext/Graphs/ProbabilityOfConnectivity.ptx
@@ -3,7 +3,7 @@
   Probability of Connectivity
   

      Probability of connectivity with n=10 and a range of p. The vertical line shows the predicted critical value.
-    " Figure 4.5: Probability of connectivity with n=10 and a range of p. The vertical line shows the predicted critical value."
+    " Probability of connectivity with n=10 and a range of p. The vertical line shows the predicted critical value."
     Line graph: probability of connectivity (n=10) vs. probability of edge (p).
       
         
The graph plots the probability of graph connectivity against the probability of an edge (p) for a graph with n=10 nodes. The x-axis, labeled 'Prob of edge (p)', is on a logarithmic scale ranging from 10^{-2.5} to 10^0=1. The y-axis, labeled 'Prob connected', ranges linearly from 0.0 to 1.0. A blue S-shaped curve illustrates the relationship, showing the probability of connectivity rising from near 0 to near 1. The steepest part of this ascent occurs around p \approx 0.23. A vertical gray line at this x-value indicates the predicted critical value for p.

@@ -11,7 +11,7 @@
   

   

      Probability of connectivity for several values of n and a range of p.
-    "Figure 4.6: Probability of connectivity for several values of n and a range of p."
+    " Probability of connectivity for several values of n and a range of p."
   Line graph: probability of connectivity vs. probability of edge (p) for n=30, 100, and 300.
       
         
This line graph compares the probability of graph connectivity for different numbers of nodes (n) as the probability of an edge (p) varies. The x-axis, labeled 'Prob of edge (p)', is on a logarithmic scale from 10^{-2.5} to 10^0=1. The y-axis, labeled 'Prob connected', ranges from 0.0 to 1.0. Three distinct S-shaped curves are presented:

diff --git a/pretext/Graphs/SelfCheck.ptx b/pretext/Graphs/SelfCheck.ptx
index 5039072..cde3b13 100755
--- a/pretext/Graphs/SelfCheck.ptx
+++ b/pretext/Graphs/SelfCheck.ptx
@@ -3,7 +3,7 @@
   Self Check
   

     A Graphical represention of a Friend Network
-    " Figure 4.6: Probability of connectivity for several values of n and a range of p."
+    " Probability of connectivity for several values of n and a range of p."
       Graph of Friend Network
     
         
An undirected graph depicting a social network with five nodes representing individuals: Josh, Kate, Jerry, Mary, and Billy-Bob. Edges connect these individuals as follows:

diff --git a/pretext/Graphs/WhatIsAGraph.ptx b/pretext/Graphs/WhatIsAGraph.ptx
index 22f0ea5..c7cd305 100755
--- a/pretext/Graphs/WhatIsAGraph.ptx
+++ b/pretext/Graphs/WhatIsAGraph.ptx
@@ -3,7 +3,7 @@
   What is a Graph?
   

      A directed graph that represents a social network.
-    " Figure 4.1: A directed graph that represents a social network. "
+    " A directed graph that represents a social network. "
           Directed graph with three nodes illustrating social network connections.
     
         
The image displays a simple directed graph consisting of three nodes, visually representing elements in a network. Edges, depicted as arrows, indicate the direction of relationships or flow between these nodes. The specific structure shown is:


From 1a94d3fd75e7a4a4bbe80da02e44db31d631878c Mon Sep 17 00:00:00 2001
From: Tristan-Raz 
Date: Fri, 16 May 2025 09:49:24 -0400
Subject: [PATCH 6/8] Removed unused alt tags to standardize the text

---
 pretext/Graphs/Generating.ptx                | 2 +-
 pretext/Graphs/GeneratingER.ptx              | 2 +-
 pretext/Graphs/NetworkX.ptx                  | 2 +-
 pretext/Graphs/ProbabilityOfConnectivity.ptx | 2 +-
 pretext/Graphs/SelfCheck.ptx                 | 2 +-
 pretext/Graphs/WhatIsAGraph.ptx              | 2 +-
 6 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/pretext/Graphs/Generating.ptx b/pretext/Graphs/Generating.ptx
index fac37a7..9abe6e8 100755
--- a/pretext/Graphs/Generating.ptx
+++ b/pretext/Graphs/Generating.ptx
@@ -3,7 +3,7 @@
   Generating Graphs
   

      A complete graph with 10 nodes.
-    " A complete graph with 10 nodes."
+    
     Complete graph with 10 nodes.
       
         
The image depicts a complete graph consisting of ten nodes. These nodes, labeled 0 through 9, are arranged in a circular pattern for visual clarity. Every node is connected to every other node by a straight edge, forming a dense network where all possible connections are present. This illustrates the fundamental property of a complete graph: full interconnectivity between all its vertices.

diff --git a/pretext/Graphs/GeneratingER.ptx b/pretext/Graphs/GeneratingER.ptx
index eb3c63c..6f9d931 100755
--- a/pretext/Graphs/GeneratingER.ptx
+++ b/pretext/Graphs/GeneratingER.ptx
@@ -3,7 +3,7 @@
   Generating ER Graphs
   

      An ER graph with n=10 and p=0.3.
-    " An ER graph with n=10 and p=0.3."
+    
 Visual representation of an Erdős-Rényi random graph with 10 nodes and specific edge connections based on p=0.3.
       
         
The image displays an Erdős-Rényi (ER) random graph. It features 10 circular nodes, which are labeled with integers from 0 to 9. These nodes are arranged in a somewhat irregular, non-grid layout across the viewing area.

diff --git a/pretext/Graphs/NetworkX.ptx b/pretext/Graphs/NetworkX.ptx
index 3881f8c..45d3ea2 100755
--- a/pretext/Graphs/NetworkX.ptx
+++ b/pretext/Graphs/NetworkX.ptx
@@ -3,7 +3,7 @@
   NetworkX
   

      An undirected graph that represents driving time between cities.
-    " An undirected graph that represents driving time between cities."
+    
     Undirected graph showing driving times between Albany, Boston, NYC, and Philly.
       
         
The image displays an undirected graph representing a road network with driving times. It features four square-shaped nodes, each labeled with a city name: Albany, Boston, NYC (New York City), and Philly (Philadelphia). These nodes are positioned on the graph to roughly approximate their actual geographical locations relative to each other.

diff --git a/pretext/Graphs/ProbabilityOfConnectivity.ptx b/pretext/Graphs/ProbabilityOfConnectivity.ptx
index b8a65d5..c5ef234 100755
--- a/pretext/Graphs/ProbabilityOfConnectivity.ptx
+++ b/pretext/Graphs/ProbabilityOfConnectivity.ptx
@@ -3,7 +3,7 @@
   Probability of Connectivity
   

      Probability of connectivity with n=10 and a range of p. The vertical line shows the predicted critical value.
-    " Probability of connectivity with n=10 and a range of p. The vertical line shows the predicted critical value."
+    
     Line graph: probability of connectivity (n=10) vs. probability of edge (p).
       
         
The graph plots the probability of graph connectivity against the probability of an edge (p) for a graph with n=10 nodes. The x-axis, labeled 'Prob of edge (p)', is on a logarithmic scale ranging from 10^{-2.5} to 10^0=1. The y-axis, labeled 'Prob connected', ranges linearly from 0.0 to 1.0. A blue S-shaped curve illustrates the relationship, showing the probability of connectivity rising from near 0 to near 1. The steepest part of this ascent occurs around p \approx 0.23. A vertical gray line at this x-value indicates the predicted critical value for p.

diff --git a/pretext/Graphs/SelfCheck.ptx b/pretext/Graphs/SelfCheck.ptx
index cde3b13..2906c16 100755
--- a/pretext/Graphs/SelfCheck.ptx
+++ b/pretext/Graphs/SelfCheck.ptx
@@ -3,7 +3,7 @@
   Self Check
   

     A Graphical represention of a Friend Network
-    " Probability of connectivity for several values of n and a range of p."
+    
       Graph of Friend Network
     
         
An undirected graph depicting a social network with five nodes representing individuals: Josh, Kate, Jerry, Mary, and Billy-Bob. Edges connect these individuals as follows:

diff --git a/pretext/Graphs/WhatIsAGraph.ptx b/pretext/Graphs/WhatIsAGraph.ptx
index c7cd305..0776bdc 100755
--- a/pretext/Graphs/WhatIsAGraph.ptx
+++ b/pretext/Graphs/WhatIsAGraph.ptx
@@ -3,7 +3,7 @@
   What is a Graph?
   

      A directed graph that represents a social network.
-    " A directed graph that represents a social network. "
+    
           Directed graph with three nodes illustrating social network connections.
     
         
The image displays a simple directed graph consisting of three nodes, visually representing elements in a network. Edges, depicted as arrows, indicate the direction of relationships or flow between these nodes. The specific structure shown is:


From 41932218f160d41b0c98fc819a6a74e0ffe108b9 Mon Sep 17 00:00:00 2001
From: Tristan-Raz 
Date: Sat, 17 May 2025 10:17:16 -0400
Subject: [PATCH 7/8] Correctly puts the text inside the image and helps
 shorten some descriptions solves issue #256

---
 pretext/Graphs/Generating.ptx                |  4 ++--
 pretext/Graphs/GeneratingER.ptx              |  4 ++--
 pretext/Graphs/NetworkX.ptx                  | 15 +++++----------
 pretext/Graphs/ProbabilityOfConnectivity.ptx | 20 ++++++++------------
 pretext/Graphs/SelfCheck.ptx                 | 18 ++++++------------
 pretext/Graphs/WhatIsAGraph.ptx              | 17 +++++++----------
 6 files changed, 30 insertions(+), 48 deletions(-)

diff --git a/pretext/Graphs/Generating.ptx b/pretext/Graphs/Generating.ptx
index 9abe6e8..5958f2e 100755
--- a/pretext/Graphs/Generating.ptx
+++ b/pretext/Graphs/Generating.ptx
@@ -3,11 +3,11 @@
   Generating Graphs
   

      A complete graph with 10 nodes.
-    
+    
     Complete graph with 10 nodes.
       
         
The image depicts a complete graph consisting of ten nodes. These nodes, labeled 0 through 9, are arranged in a circular pattern for visual clarity. Every node is connected to every other node by a straight edge, forming a dense network where all possible connections are present. This illustrates the fundamental property of a complete graph: full interconnectivity between all its vertices.

-      
+       
   

   
We'll start by generating a complete graph, which is a graph where every node is connected to every other.

   
Here's a generator function that takes a list of nodes and enumerates all distinct pairs. If you are not familiar with generator functions.

diff --git a/pretext/Graphs/GeneratingER.ptx b/pretext/Graphs/GeneratingER.ptx
index 6f9d931..3705a52 100755
--- a/pretext/Graphs/GeneratingER.ptx
+++ b/pretext/Graphs/GeneratingER.ptx
@@ -3,12 +3,12 @@
   Generating ER Graphs
   

      An ER graph with n=10 and p=0.3.
-    
+    
 Visual representation of an Erdős-Rényi random graph with 10 nodes and specific edge connections based on p=0.3.
       
         
The image displays an Erdős-Rényi (ER) random graph. It features 10 circular nodes, which are labeled with integers from 0 to 9. These nodes are arranged in a somewhat irregular, non-grid layout across the viewing area.

         
Edges, represented as lines, connect various pairs of these nodes. The graph is not complete, meaning not all possible pairs of nodes are connected. This visual sparsity is characteristic of an ER graph where edges form with a probability p (in this case, p=0.3 for n=10 nodes). For instance, the visual details show that node 3 is connected only to node 2, while other nodes, such as node 7, exhibit multiple connections to different nodes within the graph.

-      
+       
   

   
The ER graph G(n, p) contains n nodes, and each pair of nodes is connected by an edge with probability p. Generating an ER graph is similar to generating a complete graph.

   
The following generator function enumerates all possible edges and chooses which ones should be added to the graph:

diff --git a/pretext/Graphs/NetworkX.ptx b/pretext/Graphs/NetworkX.ptx
index 45d3ea2..c8c6a5d 100755
--- a/pretext/Graphs/NetworkX.ptx
+++ b/pretext/Graphs/NetworkX.ptx
@@ -3,18 +3,13 @@
   NetworkX
   

      An undirected graph that represents driving time between cities.
-    
-    Undirected graph showing driving times between Albany, Boston, NYC, and Philly.
+    
+      Undirected graph: driving times for Albany, Boston, NYC, Philly.
       
-        
The image displays an undirected graph representing a road network with driving times. It features four square-shaped nodes, each labeled with a city name: Albany, Boston, NYC (New York City), and Philly (Philadelphia). These nodes are positioned on the graph to roughly approximate their actual geographical locations relative to each other.

-        
Edges, depicted as lines, connect specific pairs of these cities, indicating direct driving routes. Each edge is labeled with the driving time in hours for that route. The connections and their labeled driving times are as follows:

-        
    
-          
  • Albany to Boston: 3 hours
    • 
-          
  • Albany to NYC: 4 hours
    • 
-          
  • Boston to NYC: 4 hours
    • 
-          
  • NYC to Philly: 2 hours
    • 
-        

+        
The image displays an undirected graph representing a road network with driving times. It features four square-shaped nodes, labeled with city names: Albany, Boston, NYC (New York City), and Philly (Philadelphia), positioned to roughly approximate their geographical locations.

+        
Edges, as lines, connect these cities, indicating direct driving routes. Each edge is labeled with the driving time in hours. Specifically, the connections are: Albany to Boston (3 hours), Albany to NYC (4 hours), Boston to NYC (4 hours), and NYC to Philly (2 hours).

       
+    
   

   
To represent graphs, we'll use a package called NetworkX, which is the most commonly used network library in Python.

   
We can create a directed graph by importing NetworkX (usually imported as nx) and instantiating nx.DiGraph:

diff --git a/pretext/Graphs/ProbabilityOfConnectivity.ptx b/pretext/Graphs/ProbabilityOfConnectivity.ptx
index c5ef234..ee7209f 100755
--- a/pretext/Graphs/ProbabilityOfConnectivity.ptx
+++ b/pretext/Graphs/ProbabilityOfConnectivity.ptx
@@ -3,25 +3,21 @@
   Probability of Connectivity
   

      Probability of connectivity with n=10 and a range of p. The vertical line shows the predicted critical value.
-    
+    
     Line graph: probability of connectivity (n=10) vs. probability of edge (p).
       
         
The graph plots the probability of graph connectivity against the probability of an edge (p) for a graph with n=10 nodes. The x-axis, labeled 'Prob of edge (p)', is on a logarithmic scale ranging from 10^{-2.5} to 10^0=1. The y-axis, labeled 'Prob connected', ranges linearly from 0.0 to 1.0. A blue S-shaped curve illustrates the relationship, showing the probability of connectivity rising from near 0 to near 1. The steepest part of this ascent occurs around p \approx 0.23. A vertical gray line at this x-value indicates the predicted critical value for p.

-      
+       
   

   

      Probability of connectivity for several values of n and a range of p.
-    " Probability of connectivity for several values of n and a range of p."
-  Line graph: probability of connectivity vs. probability of edge (p) for n=30, 100, and 300.
+    " Probability of connectivity for several values of n and a range of p."
+  Connectivity probability vs. edge probability (p) for n=30, 100, 300.
       
-        
This line graph compares the probability of graph connectivity for different numbers of nodes (n) as the probability of an edge (p) varies. The x-axis, labeled 'Prob of edge (p)', is on a logarithmic scale from 10^{-2.5} to 10^0=1. The y-axis, labeled 'Prob connected', ranges from 0.0 to 1.0. Three distinct S-shaped curves are presented:

-        
    
-          
  • A dark blue curve for n=30.
    • 
-          
  • A medium blue curve for n=100.
    • 
-          
  • A light blue curve for n=300.
    • 
-        

-        
The graph illustrates that as the number of nodes (n) increases, the S-shaped curve representing the transition to connectivity shifts to the left (towards lower values of p) and the transition becomes steeper or more abrupt. Each curve is accompanied by a faint vertical line indicating its respective critical point for p.

-      
+        
This line graph shows how graph connectivity probability changes with varying numbers of nodes (n) and edge probability (p). The x-axis, 'Prob of edge (p)', is logarithmic (10^{-2.5} to 10^0). The y-axis, 'Prob connected', ranges from 0.0 to 1.0.

+        
Three S-shaped curves are shown: a dark blue curve for n=30, a medium blue curve for n=100, and a light blue curve for n=300. Each curve has a faint vertical line at its critical point for p.

+        
As n increases, the S-curve (transition to connectivity) shifts left towards lower p values and becomes steeper, indicating a more abrupt transition.

+       
   

   
For given values of n and p, we would like to know the probability that G(n, p) is connected. We can estimate it by generating a large number of random graphs and counting how many are connected. Here's how:

   
def prob_connected(n, p, iters=100):
diff --git a/pretext/Graphs/SelfCheck.ptx b/pretext/Graphs/SelfCheck.ptx
index 2906c16..f57421d 100755
--- a/pretext/Graphs/SelfCheck.ptx
+++ b/pretext/Graphs/SelfCheck.ptx
@@ -3,19 +3,13 @@
   Self Check
   

     A Graphical represention of a Friend Network
-    
+    
       Graph of Friend Network
-    
-        
An undirected graph depicting a social network with five nodes representing individuals: Josh, Kate, Jerry, Mary, and Billy-Bob. Edges connect these individuals as follows:

-        
    
-          
  • Josh is connected to Billy-Bob.
    • 
-          
  • Kate is connected to Jerry, Mary, and Billy-Bob.
    • 
-          
  • Jerry is connected to Kate and Billy-Bob.
    • 
-          
  • Mary is connected to Kate and Billy-Bob.
    • 
-          
  • Billy-Bob is connected to Josh, Kate, Jerry, and Mary, acting as a central connector.
    • 
-        

-        
The connections are mutual, indicating friendships or bidirectional relationships.

-      
+  
+    
An undirected graph depicts a social network with five nodes: Josh, Kate, Jerry, Mary, and Billy-Bob. Edges show connections between these individuals.

+    
Josh is connected to Billy-Bob. Kate is connected to Jerry, Mary, and Billy-Bob. Jerry is connected to Kate and Billy-Bob; Mary is also connected to Kate and Billy-Bob. Billy-Bob connects to Josh, Kate, Jerry, and Mary, acting as a central connector.

+    
The connections are mutual, indicating friendships or bidirectional relationships.

+   
   

   
     
diff --git a/pretext/Graphs/WhatIsAGraph.ptx b/pretext/Graphs/WhatIsAGraph.ptx
index 0776bdc..e209768 100755
--- a/pretext/Graphs/WhatIsAGraph.ptx
+++ b/pretext/Graphs/WhatIsAGraph.ptx
@@ -3,17 +3,14 @@
   What is a Graph?
   

      A directed graph that represents a social network.
-    
-          Directed graph with three nodes illustrating social network connections.
-    
-        
The image displays a simple directed graph consisting of three nodes, visually representing elements in a network. Edges, depicted as arrows, indicate the direction of relationships or flow between these nodes. The specific structure shown is:

-        
    
-          
  • Two of the nodes have a mutual (bidirectional) connection, with arrows pointing from each of these two nodes to the other (Bob and Alice).
    • 
-          
  • Both of these mutually connected nodes also have outgoing arrows pointing towards the third node (Chuck).
    • 
-          
  • The third node (Chuck) is a recipient in these relationships; it only has incoming arrows from the other two nodes and possesses no outgoing arrows.
    • 
-        

-        
This visual structure corresponds to the example given in the text where 'Alice' and 'Bob' follow each other, and both also follow 'Chuck', while 'Chuck' does not follow anyone back.

+    
+      Directed three-node graph showing social network connections.
+      
+        
The image displays a simple directed graph with three nodes, visually representing network elements. Edges, as arrows, show the direction of relationships. The nodes can be identified as Alice, Bob, and Chuck based on the text's example.

+        
A mutual, bidirectional connection exists between two nodes (Alice and Bob), shown by arrows pointing from each to the other. Both of these nodes also have outgoing arrows directed towards the third node (Chuck).

+        
The third node (Chuck) only has incoming arrows from Alice and Bob and no outgoing arrows. This structure illustrates the example where Alice and Bob follow each other, both follow Chuck, and Chuck follows no one back.

       
+    
   

   
To most people a graph is a visual representation of data, like a bar chart or a plot of stock prices over time. That's not what this chapter is about.

   
In this chapter, a graph is a representation of a system that contains discrete, interconnected elements. The elements are represented by nodes — also called vertices – and the interconnections are represented by edges.


From 88a7a7accefa749b6ddf537e80187c9db6f58b23 Mon Sep 17 00:00:00 2001
From: Tristan-Raz 
Date: Tue, 20 May 2025 09:22:06 -0400
Subject: [PATCH 8/8] Removed missed alt tag fixes issue #256

---
 pretext/Graphs/ProbabilityOfConnectivity.ptx | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/pretext/Graphs/ProbabilityOfConnectivity.ptx b/pretext/Graphs/ProbabilityOfConnectivity.ptx
index ee7209f..84feb32 100755
--- a/pretext/Graphs/ProbabilityOfConnectivity.ptx
+++ b/pretext/Graphs/ProbabilityOfConnectivity.ptx
@@ -11,7 +11,7 @@
   

   

      Probability of connectivity for several values of n and a range of p.
-    " Probability of connectivity for several values of n and a range of p."
+    
   Connectivity probability vs. edge probability (p) for n=30, 100, 300.
       
         
This line graph shows how graph connectivity probability changes with varying numbers of nodes (n) and edge probability (p). The x-axis, 'Prob of edge (p)', is logarithmic (10^{-2.5} to 10^0). The y-axis, 'Prob connected', ranges from 0.0 to 1.0.