+Graph Theory

Themes

Discover better, more realistic graph generators. Discover more realistic algorithms for various tasks like finding shortest path.

Applications

Epidemology. Spread of ideas. Movie/ book recommendation.

Electric network analysis

Kirchoff current (y) and voltage (x) laws, Ohm’s law: edge current sources f: $Ax=b,A^{T}y=f,y=CAx$. Elimination in A: rows independent if not loop; Formation of spanning tree; so r=n-1. So, left nullspace basis = loops = m-n+1. Implies Euler Formula: n - m + loops = 1.