# Load Centrality

#### Definition

The load centrality of a node is the fraction of all shortest paths that pass through that node. Load centrality is slightly different than betweenness.

Goh et al.'s load centrality (as reformulated by Brandes (2008)) is a betweenness-like measure defined through a hypothetical flow process. Specifically, it is assumed that each vertex sends a unit of some commodity to each other vertex to which it is connected (without edge or vertex capacity constraints), with routing based on a priority system: given an input of flow x arriving at vertex v with destination v', v divides x equally among all neigbors of minumum geodesic distance to the target. The total flow passing through a given v via this process is defined as v's load. Load is a potential alternative to betweenness for the analysis of flow structures operating well below their capacity constraints. [CARTER T. BUTTS, 2014]

Goh et al.'s load centrality (as reformulated by Brandes (2008)) is a betweenness-like measure defined through a hypothetical flow process. Specifically, it is assumed that each vertex sends a unit of some commodity to each other vertex to which it is connected (without edge or vertex capacity constraints), with routing based on a priority system: given an input of flow x arriving at vertex v with destination v', v divides x equally among all neigbors of minumum geodesic distance to the target. The total flow passing through a given v via this process is defined as v's load. Load is a potential alternative to betweenness for the analysis of flow structures operating well below their capacity constraints. [CARTER T. BUTTS, 2014]

#### References

- A HAGBERG, D. S., P SWART. Exploring Network Structure, Dynamics, and Function using NetworkX. In: G VAROQUAUX, T. V., J MILLMAN, ed. Proceedings of the 7th Python in Science conference (SciPy 2008), 2008. 11-15.
- BRANDES, U. 2008. On variants of shortest-path betweenness centrality and their generic computation. Social Networks, 30, 136-145.
- CARTER T. BUTTS (2014). sna: Tools for Social Network Analysis. R package version 2.3-2. http://CRAN.R-project.org/package=sna
- CSARDI, G. & NEPUSZ, T. 2006. The igraph software package for complex network research. InterJournal, Complex Systems, 1695. [http://igraph.org]
- GOH, K.-I., KAHNG, B. & KIM, D. 2001. Universal behavior of load distribution in scale-free networks. Physical Review Letters, 87, 278701.