# Metrics

`netseg` currently supports the following metrics:

| Metric Name | Year | Network Type *Original* |Network Type `netseg` |Multiple Groups | <div style="width: 180px;">Theoretical Complexity</div>| <div style="width: 200px;">Range</div> |
| :--- | :--- | :--- | :--- | :----- |:----- | :---------|
| Boundary Connectivity | 2013 | Undirected |Both|Yes | O(M * (V + E)) | [-0.5, 0.5]|
| Random Walk Controversy | 2018 | Undirected |Both| Yes | O(M * S * L) | [-1, 1] |
| Dipole Moment | 2015 | Undirected  |Both| No (Two Only) | O(M * I * E) | [0, 1]|
| Freeman's Segregation Index | 1978 | Undirected  |Both| Yes | O(M * (V + E)) | [0, 1]| 
| Krackhardt E-I | 1988 | Both | Both|Yes | O(M * (V + E)) | [-1, 1]|
| Segregation Matrix Index | 1997 | Directed |Both| Yes | O(M * (V + E))| [-1, 1]|
| Coleman's Homophily Index | 1958 | Directed  |Both| Yes | O(M * K * (V + E)) | [-1, 1]|
| GAM Index | 1989 | Both |Both| Yes | O(M * (V + E + K²)) | [$-\frac{1}{G - 1}$, 1] |
| ORWG | 2001 | Both | Both|Yes | O(M * (V + E))|[0, $\infty$) |
| Spectral Segregation Index | 2007 | Undirected |Undirected| Yes | O(V + M * V³) |[0, ∞) |
| Assortativity Coefficient | 2003 | Both | Both|Yes | O(M * (V + E)) | [$-\frac{\sum a_i b_i}{1 - \sum a_i b_i}$, 1] |

*Note: Complexity notations are defined as follows: **V**: Vertices, **E**: Edges, **M**: Null Models, **S**: Simulations, **L**: Walk Length, **I**: Iterations, **K**: Unique Groups. V, E, and M are applicable to all metric complexities where listed.* **Given complexities are adjusted for the worst case for Random Walk Controversy, Dipole Moment and SSI. If null models are not given specifically, M = 1.**

**Note:** ```netseg``` implementation is almost always $V \log V$ instead of $V$ due to guardrails and sorting of the nodes. Above notation is the metric itself. 

**Note:** `netseg` extends the measures and allows undirected measures to be applied to directed networks and vice versa. In this case it raises a warning to notify the user.

To propose a new metric for inclusion, please contact the authors with a concise summary of the measure, its computational complexity, your proposed implementation, and a clear explanation of how it uniquely differentiates itself from the existing suite of metrics.



```{toctree}
:maxdepth: 2

ssi
coleman
boundary
krackhardt
rwc
gamq
freeman
dipole
smi
orwg
assort