Metrics

netseg currently supports the following metrics:

Metric Name	Year	Network Type Original	Network Type netseg	Multiple Groups	Theoretical Complexity	Range
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.

• Spectral Segregation Index
  • Basics
  • Multiple Groups
  • Example
  • References
• Coleman’s Homophily Index
  • Basic Usage
  • Multiple Groups
  • Notes on Null Model Selection
  • Example
  • References
• Boundary Connectivity
  • Boundary Nodes
  • Basic Usage
  • Relaxed Definition
  • Multiple Groups
  • Directed Networks
  • Example
  • References
• Krackhardt’s EI Score
  • Basic Usage
  • Multiple Groups
  • Example
  • References
• Random Walk Controversy
  • Basic Usage
  • Directed Graphs
  • Selecting Influential Nodes
  • Multiple Groups
  • Parameter Selection
  • Number of Simulations
  • Example
  • References
• Gupta, Anderson and May’s Q
  • Basic Usage
  • Multiple Groups
  • Example
  • References
• Freeman’s Segregation Index
  • Basic Usage
  • Multiple Groups
  • Example
  • References
• Dipole Moment
  • Basic Usage
  • Picking Influential Nodes
  • References
• Segregation Matrix Index
  • Basic Usage
  • Multiple Groups
  • Example
  • References
• Odds Ratio for Within Group Ties
  • Basic Usage
  • Multiple Groups
  • Example
  • References
• Assortativity Coefficient
  • Basic Usage
  • Multiple Groups
  • Example
  • References