Notebook

Networks¶

In [2]:

%matplotlib inline
%config InlineBackend.figure_format='retina'
# import libraries
import numpy as np
import matplotlib as mp
import pandas as pd
import matplotlib.pyplot as plt
import laUtilities as ut
import slideUtilities as sl
import demoUtilities as dm
import pandas as pd
from importlib import reload
from datetime import datetime
from IPython.display import Image
from IPython.display import display_html
from IPython.display import display
from IPython.display import Math
from IPython.display import Latex
from IPython.display import HTML
print('')

In [3]:

%%html
<style>
 .container.slides .celltoolbar, .container.slides .hide-in-slideshow {
    display: None ! important;
}
</style>

%Set up useful MathJax (Latex) macros. %See http://docs.mathjax.org/en/latest/tex.html#defining-tex-macros %These are for use in the slideshow $\newcommand{\mat}[1]{\left[\begin{array}#1\end{array}\right]}$ $\newcommand{\vx}{{\mathbf x}}$ $\newcommand{\hx}{\hat{\mathbf x}}$ $\newcommand{\vbt}{{\mathbf\beta}}$ $\newcommand{\vy}{{\mathbf y}}$ $\newcommand{\vz}{{\mathbf z}}$ $\newcommand{\R}{{\mathbb{R}}}$ $\newcommand{\vu}{{\mathbf u}}$ $\newcommand{\vv}{{\mathbf v}}$ $\newcommand{\vw}{{\mathbf w}}$ $\newcommand{\col}{{\operatorname{Col}}}$ $\newcommand{\nul}{{\operatorname{Nul}}}$ $\newcommand{\vb}{{\mathbf b}}$ $\newcommand{\va}{{\mathbf a}}$ $\newcommand{\ve}{{\mathbf e}}$ $\newcommand{\setb}{{\mathcal{B}}}$ $\newcommand{\rank}{{\operatorname{rank}}}$ $\newcommand{\vp}{{\mathbf p}}$

\newcommand{\mat}[1]{\left[\begin{array}#1\end{array}\right]} \newcommand{\vx}{{\mathbf x}} \newcommand{\hx}{\hat{\mathbf x}} \newcommand{\vbt}{{\mathbf\beta}} \newcommand{\vy}{{\mathbf y}} \newcommand{\vz}{{\mathbf z}} \newcommand{\vb}{{\mathbf b}} \newcommand{\vu}{{\mathbf u}} \newcommand{\vv}{{\mathbf v}} \newcommand{\vw}{{\mathbf w}} \newcommand{\va}{{\mathbf a}} \newcommand{\ve}{{\mathbf e}} \newcommand{\vp}{{\mathbf p}} \newcommand{\R}{{\mathbb{R}}} \newcommand{\col}{{\operatorname{Col}}} \newcommand{\nul}{{\operatorname{Nul}}} \newcommand{\rank}{{\operatorname{rank}}} \newcommand{\setb}{{\mathcal{B}}}

Network analysis - potentials, edge-incidence, spanning trees

Based on Strang Ch 2.5 and Spielman/Srivastava

And, properties of the Laplacian (if time) - graph embedding