This document summarizes and compares different techniques for thresholding weighted networks to uncover core structures. It discusses global thresholding, dyadic thresholding, and ego-centric thresholding. Results show that ego-centric thresholding eliminated the most ties at significance levels and made the most sense for the dataset of website browsing data. Global thresholding performed the weakest. The appropriate choice between dyadic and ego-centric thresholding depends on which null model fits the particular context best.

1. WHAT COUNTS AS A
WEAK TIE?Subhayan Mukerjee and Sandra Gonzalez-Bailon
68th Conference of International Communication Association,
Prague, 2018
A Comparison of
Thresholding Techniques to
Analyze Weighted Networks

2. WHAT IS
THRESHOLD
ING?
The removal of edges to uncover the “core” of the network
figures courtesy Andrew Zalesky

3. TYPES OF
THRESHOLDING
- Normalize weights to [0,1]
- Set a threshold τ ∈ [0,1]
- Remove edges with norm.
weight <= τ
- Progressively increase τ
Global Thresholding
(Borge-Holthoefer and González-Bailón,
2017)
eg. De Choudhury, Mason, Hofman, & Watts,
2010
Eguíluz, Chialvo, Cecchi, Baliki, & Apkarian,
2005
Allesina, Bodini, & Bondavalli, 2006
Dyadic Thresholding
(Ronen, Gonçalves, Hu, Vespignani, Pinker &
Hidalgo, 2014)
- Is a tie between two nodes
stronger than what is expected
by chance?
𝛷𝑖𝑗 =
𝐷𝑖𝑗 𝑁 − 𝐴𝑖𝐴𝑗
𝐴𝑖 𝐴𝑗(𝑁 − 𝐴𝑖)(𝑁 − 𝐴𝑗)
𝑡 =
𝛷𝑖𝑗 max(𝐴𝑖, 𝐴𝑗) − 2
1 − 𝛷𝑖𝑗
2
eg. Majó-Vázquez, Cardenal, & González-Bailón
(2017)
Mukerjee, Majo-Vázquez, & Gonzalez-Bailon,
(2018)
Ego centric thresholding
(disparity filter)
(Serrano, Boguna, & Vespignani, 2009)
- Eliminates edges without destroying the
multi-scale nature of real world
networks. Compare normalized weights
to a simulated network built by
randomly assigning normalized weights
from a uniform distribution
𝑠𝑖 =
𝑖
𝑤𝑖𝑗
𝑝𝑖𝑗 = 𝑤𝑖𝑗 𝑠𝑖
𝛼𝑖𝑗 = 1 − 𝑝𝑖𝑗
𝑘−1
eg. Ahn, Ahnert, Bagrow, & Barabási, 2011
Del Vicario, Zollo, Caldarelli, Scala, &
Quattrociocchi, 2017 Olson & Neal, 2015

4. DATA
- Obtained from comScore
- Website browsing data in the US and the UK
- Two important statistics
- Audience reach (number of users visiting each website)
- Cross-visiting (number of users visiting each pair of sites)

5. RESULTS

7. CONCLUSIONS
1. The weight distribution greatly affects the results
2. The ego-centric thresholding eliminates the largest number of ties
for a significance level
3. In the context of this dataset, the ego centric thresholding makes
the most sense (local disparities are high owing to skew of degree
and heterogeneity of reach)
4. Global thresholding is the weakest of the options
5. Finally, between dyadic thresholding vs ego centric thresholding –
which null models makes more sense in a particular context –
determines which can work better.

8. subhayan.mukerjee@asc.upe
nn.edu@wrahoolTHANK YOU!
QUESTIONS?