notesum.ai

Published at December 6

physics.soc-ph

cs.SI

Released Date: December 6, 2024

Authors: Christian Franssen¹, Joost Berkhout², Bernd Heidergott¹

Aff.: ¹Dept. Operations Analytics, VU Amsterdam, The Netherlands; ²Dept. of Mathematics, VU Amsterdam, The Netherlands

Feature function	Symbol	Description	Definition
In-strength	$s^{-}=(s_{i}^{-})_{i\in V}$	The sum of link weights reaching each node $i$ .	(1)
Out-strength	$s^{+}=(s_{i}^{+})_{i\in V}$	The sum of link weights leaving each node $i$ .	(2)
Reciprocity	$r$	The extent to which nodes reciprocate incoming	Appendix A.1
		links.
Triangular	$c$	The extent to which nodes form closed triplets.	Appendix A.2
closures
Modularity	$Q$	The extent to which nodes are grouped in	Appendix A.3
		communities or clusters.
Assortativity	$\rho$	Tendency for nodes to link with others that are	Appendix A.4
		similar in node covariates or a function over the
		network itself (e.g., node strengths).
Stationary	$\pi=(\pi_{i})_{i\in V}$	The long-run fraction of time the random walker	Appendix A.5
$\text{distribution}^{\dagger}$		spends at each node $i$ .
Kemeny	$K$	The expected time to reach a $\pi$ -randomly drawn	Appendix A.6
$\text{constant}^{\dagger}$		node from any arbitrary node.
Effective graph	$R$	The sum of electrical resistances in a resistor	Appendix A.7
resistance		network with edge weights as conductances.