> For the complete documentation index, see [llms.txt](https://measures.gitbook.io/multiple-measures/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://measures.gitbook.io/multiple-measures/progress/week-1.md).

# Week 1

Literature reviews, overview of the project.

## Meeting

![sketch](https://3721256156-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LjlQrTHR3_jKnoq29j0%2F-LjuIvfZBR9CjppR5DiD%2F-LjuL9NOp_2afcImJfwH%2Fsketch.png?alt=media\&token=297a60cd-4f99-4598-a339-39aedd9bfe87)

* the idea is to use the **dynamic** measures to see the graph
* for HD features or combined features, using a connected scatter plot seems interesting
* narrow down the design, and focus more on the problem itself rather than users

## Graph Measures

### Measure Level

* time: snapshot → period → lifetime
* component: local → subgraph → global

|          | local                 | subgraph              | global                |
| -------- | --------------------- | --------------------- | --------------------- |
| snapshot | single value          | single value          | single value          |
| period   | aggr, series, derived | aggr, series, derived | aggr, series, derived |
| lifetime | aggr, series, derived | aggr, series, derived | aggr, series, derived |

{% hint style="info" %}
"aggregated value" refers to the calculated metric value from an aggregated graph. "series value" means a value sequences for each snapshot during the period. And "derived value" is the derived value from series value, such as extremes, average value, deviance, trend,  stability, fastest increase, etc.
{% endhint %}

### Details

**Global**

* Static
  * count, ratio
    * number of nodes, active nodes, links, node pairs,  connected components, motifs (triads, cliques...), clusters, activation, redundancy
    * clustering coefficient
  * extreme
    * diameter, 
  * average
    * characteristic path length ( shortest path length), efficiency (1/shortest path)
  * others
    * modularity
* Dynamic
  * global volatility

**Local**

* Static
  * centrality: identify the most important vertex or link in a graph
    * degree, strength (sum of weight)
    * eccentricity (max d\_ij)
    * closeness (average shortest path length)
    * betweenness
  * others
    * pagerank, redundancy
* Dynamic
  * volatility: sum presence variance of links to a node
  * activation: count of new connections

**High-Dimensional Features (learned from data)**

Deepwalk, Graph2Vec, SDNE, matrix factorization, persistent diagram, adjacent matrix