Networks and the Epidemiology of Infectious Disease

Table 1

Common notation.

Concept/Measure	Other common names	Our notation	Other common notation
Network	Graph	𝐺
Node	Vertex, point, site, actor	𝑛	𝑣
Edge	Link, tie, bond	𝑙	𝑒
Adjacency matrix	Connectivity matrix	𝐺𝑖𝑗	𝑎𝑖𝑗,𝐴𝑖𝑗
Number of nodes	Size of network	𝑁	𝑛,𝑆
Number of edges	Graph size	𝐿	𝑒, 𝑙
Centrality		𝐶
Degree	Connectivity	𝑘	𝑑, 𝐶𝑑
Betweenness		𝐵𝑖	bet𝑖, 𝐶𝑏
Degree distribution	Connectivity distribution	𝑃(𝑘)	𝑃𝑘,𝑝𝑘
Shortest path distance	Geodesic distance	𝐷𝑖,𝑗	𝑑𝑖,𝑗
Clustering	transitivity	𝜙	𝑐, Φ
Number of nodes of type A		[𝐴]	𝑛𝐴,𝑁𝐴
Number of 𝐴−𝐵 pairs		[𝐴𝐵]	𝑛𝐴𝐵,𝑁𝐴𝐵
Diameter	Maximal shortest path	Diam(𝐺)	max(𝐷𝑖,𝑗)