# Graph

Graph A graph $\mathcal G$ has nodes $\mathcal V$ and edges $\mathcal E$, $$\mathcal G = ( \mathcal … Local Statistics Node Degree Node Degree Node degree of a node u$$ d_u = \sum_{v\in \mathcal V} …

The Ratio Cut Graph Cuts Cut For a subset of nodes $\mathcal A\subset \mathcal V$, with the rest of …
The Katz index is $$\mathbf S_{\text{Katz}}[u,v] = \sum_{i=1}^\infty \beta^i \mathbf A^i[u, v],$$ …
Random Walk Construct a stochastic transfer matrix $P$ by normalizing the adjacency matrix $\mathbf … For two graphs,$\mathcal G$and$\mathcal H$, the two graphs are isomorphism on the following … The Adamic Adar (AA) index is1 $$\mathbf S_{\text{AA}}[v_1,v_2] = \sum_{u\in\mathcal N(u) \cap … The Resource Allocation (RA) index is$$ \mathbf S_{\text{RA}}[v_1,v_2] = \sum_{u\in\mathcal N(u) … The Salton index is $$\mathbf S_{\text{Salton}}[u,v] = \frac{ 2\lvert \mathcal N (u) \cap \mathcal … The Sorensen index is$$ \mathbf S_{\text{Sorensen}}[u,v] = \frac{ 2\lvert \mathcal N (u) \cap … Betweenness centrality of a node$v$is measurement of how likely the shortest path between two … Given a graph with adjacency matrix$\mathbf A\$, the eigenvector centrality is $$\mathbf e_u = … A graph \mathcal G can be represented with an adjacency matrix \mathbf A. Multiplication of … Cut For a subset of nodes \mathcal A\subset \mathcal V, with the rest of nodes \bar {\mathcal A} … Laplacian is a useful representation of graphs. The unnormalized Laplacian is$$ \mathbf L = \mathbf …