# Graph

Some basic concepts about 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} …

Some basic concepts about graph and traditional algorithms

The Ratio Cut Graph Cuts Cut For a subset of nodes $\mathcal A\subset \mathcal V$, with the rest of …

Node Classification Given graph that has incomplete attribute labeling of the nodes, predict the …

mind the data structure: here comes the graph

stateDiagram-v2 with_spectral_matrix_representation: Spectral Matrix Representation …

For a given graph $\mathcal G$, we have an attribute on each node, denoted as $f_v$. All the node …

The Katz index is $$\mathbf S_{\text{Katz}}[u,v] = \sum_{i=1}^\infty \beta^i \mathbf A^i[u, v],$$ …

From Katz Index to LHN Index Katz Index Graph Global Overlap Measure: Katz Index The Katz index is …

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\$. There are some nice …