# 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,
$${k}_{s \in \mathrm{1,2},\dots n}$$
Number of adjacent edges $$\sum\nolimits_{j = 1}^{N} {A_{s,j} }$$ 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 