Graph Theory

Dated Mar 21, 2020; last modified on Sun, 14 Mar 2021

I have this rosy view of graph theory being elegant, but I’ve never set aside time to dive deeply into it. One day…

Random Link ¯\_(ツ)_/¯

Oct 13, 2021

Towards a Collaborative Web Browser 3 min; updated Feb 12, 2023

One of the grand dreams of the web is bringing people together so that they may find relevant information.

Sometimes this is implicit, e.g. Google Search’s PageRank learns from inter-page links which are mostly made by people, but there may be room for explicit collaboration when navigating the web. This section explores such explicit attempts.

#lost-in-hyperspace

A Group Asynchronous Browsing (GAB) Server

Premise: Users submit their subject hierarchies (bookmarks) to the GAB server. The GAB server then forms a multitree from these hierarchies.

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Nov 13, 2017

Modeling Influence with Graphs 3 min; updated Feb 12, 2023

Graphs, \(G = (V, E) \)	\(N \times N \) Adjacency Matrix	\(N \times L \) Incidence Matrix
	\(A = \begin{bmatrix}0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1\end{bmatrix} \)	\(\hat{A} = \begin{bmatrix}1 & 0 & -1 & 0 \\ -1 & 1 & 0 & 0 \\ 0 & -1 & 1 & -1 \\ 0 & 0 & 0 & 1\end{bmatrix} \)
\( V \) = set of \( N \) nodes \( E \) = set of \( L \) links	\( A_{ij} = 1 \) iff \( (i, j) \in E \) Note that \(A\) need not be symmetric for directed graphs.	For a directed graph, \( A_{ij} \) is \(1\) if \( i \) starts at \( j \); \(-1\) if \(i\) ends at \(j\), and \(0\) otherwise. For an undirected graph, \(A_{ij}\) is \(1\) if \(i\) on \(j\), and \(0\) otherwise.

Measurements of Node Importance

Degree Centrality of Node \(i\)

For undirected graphs, this is the number of nodes connecting to node \(i\).

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Jan 27, 2020

Tech and Democracy 5 min; updated Sep 5, 2022

Political Ads

Cambridge Analytica (CA) paid people to take in-app survey; mined FB profile data including friends’ data; crafted tailored sensitive ads to sway-able voters. Elections are about emotions, not facts. Data science and social media can help us make sense of and manipulate the chaos.

An alternative argument. Political misinformation is:

Weak in high profile partisan races because pre-existing beliefs hardly change
Strong when people don’t have string pre-existing opinions, e.g. misinformation about voter ID laws causing people to stay home from the polls

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