# Table 1 Social Network Estimates used to describe the Node Position of Index Individuals ($$s\in \{\mathrm{1,2},..n\}$$) within the Kampala Network

Statistic

Definition

Equation

Notation

Node degree,

$${k}_{s \in \mathrm{1,2},\dots n}$$

$$\sum\nolimits_{j = 1}^{N} {A_{s,j} }$$

Adjacency matrix, $${A}_{ij}=1$$, if we identified contact between $$i,j$$

Betweenness,

$${b}_{s\in \mathrm{1,2},...n}$$

Number of times node is on shortest path between pairs of other nodesa

$$\sum\nolimits_{u \ne s \ne v} {\frac{{\sigma_{uv} \left( s \right)}}{{\sigma_{uv} }}}$$

$${\sigma }_{uv}$$ is the total number of shortest paths from node $$u$$ to $$v$$ and $${\sigma }_{uv}\left(s\right)$$ is the number of those paths that pass through $$s$$

Closeness,

$${c}_{s\in \mathrm{1,2},...n}$$

Inverse of the average length of shortest path to all other nodesa

$$\frac{1}{{\sum\nolimits_{i \ne s} {d_{si} } }}$$

$${d}_{si}$$ is the network distance between nodes $$s$$ and $$i$$

Distance to TB case,

$${y}_{s\in \mathrm{1,2},...n}$$

Network distance to a TB casea

$${\text{min}}\left( {d_{st, t \ne s} } \right)$$

$$t$$ is the set of TB cases

1. aNetwork distance, closeness, and betweenness were calculated within the giant component because path length is not defined for disconnected graphs