Contact-Omission in Network Analysis

• Contact-omission (CO) is the systematic loss or omission of relational data in networks, leading to false negatives in CSS elicitation and contact tracing.
• CO quantitatively affects network estimation and epidemic modeling by altering key metrics like network density, error tradeoffs, and outbreak dynamics.
• Techniques such as the ROC-based Threshold Method help mitigate CO effects, improving network reconstruction and informing public health interventions.

Contact-omission (CO) refers to the systematic loss or omission of relational, contact, or edge information in network data, with critical relevance in both the cognitive social structure (CSS) literature and stochastic agent-based modeling of epidemic processes. CO emerges either as a perceptual error—manifesting as false negatives when individuals fail to recall actual ties in CSS elicitation—or as a structural shortfall in contact tracing, where specific contact events are not identified, even though case trajectories are otherwise reconstructed. Empirically, CO affects key properties of reconstructed or inferred networks, impacting accuracy metrics, estimation workflows, and, in epidemiological settings, the ability of containment strategies to suppress transmission chains.

1. Formal Definitions of Contact-Omission

In CSS network analysis, contact-omission is defined as the failure to recognize or report an existing tie. Let $A$ denote the true directed network adjacency matrix on $N$ actors: $$A_{jk} = \begin{cases} 1, & \text{if there is a true tie }j \to k \ 0, & \text{otherwise} \end{cases}$$ A respondent’s perception matrix $P^{(i)}$ encodes their beliefs about all possible ties. The omission (Type 2, or CO) error rate for a respondent $i$ is: $$\mathrm{CO}_i = \frac{\sum_{j \neq k} \mathbf{1}\{A_{jk}=1,\, P_{jk}^{(i)}=0\}}{\sum_{j \neq k} A_{jk}}$$ For agent-based epidemic contact tracing, CO refers to the scenario where, for a confirmed infector $j$, a fraction of their documented contacts in various social layers $\ell$ (e.g., household, workplace) are omitted: $$X_{j,i}^{(\ell)} \sim \mathrm{Bernoulli}(p^{(\ell)})$$ with $X_{j,i}^{(\ell)}=1$ signifying omission of the contact, and $N$0 the contact-omission probability for layer $N$1 (Chae et al., 21 Jan 2026).

2. Empirical Characterization and Correlates

Across canonical CSS datasets, mean omission rates ($N$2) are substantially higher (0.539–0.723) than mean commission rates ($N$3, 0.028–0.136), reflecting the sparsity characteristic of most real-world social networks. The within-actor correlation between omission and commission rates is strongly negative (–0.68 to –0.94), indicating a tradeoff: individuals with low false-positive rates tend to exhibit higher omission rates, and vice versa. When ranking actors by overall error, those with low total errors have mistakes dominated by omissions, while high-error actors increasingly display commission-dominated error profiles (Yenigun et al., 2016).

In epidemic simulations, CO is modeled as Bernoulli edge loss applied independently to each documented contact per infector and layer. Scenario-specific omission rates (e.g., selective SCO, uniform UCO) introduce omission as a continuous parameter, not a binary state (Chae et al., 21 Jan 2026).

3. Methodologies for Modeling and Estimating Networks under CO

In CSS analysis, the ROC-based Threshold Method (RTM) aggregates sampled perception slices to estimate the whole network. The method:

1. Samples $N$4 CSS slices; computes average density $N$5.
2. For each threshold $N$6, computes estimated false-positive ($N$7) and false-negative ($N$8) rates on the knowledge region.
3. Chooses $N$9, with $$A_{jk} = \begin{cases} 1, & \text{if there is a true tie }j \to k \ 0, & \text{otherwise} \end{cases}$$0 to counteract sparsity bias.
4. Aggregates using a Fixed-Threshold Method at $$A_{jk} = \begin{cases} 1, & \text{if there is a true tie }j \to k \ 0, & \text{otherwise} \end{cases}$$1.

This approach requires minimal user input and, by tuning $$A_{jk} = \begin{cases} 1, & \text{if there is a true tie }j \to k \ 0, & \text{otherwise} \end{cases}$$2, allows for cost-sensitive control over the omission–commission tradeoff (Yenigun et al., 2016).

In agent-based epidemic models, CO is operationalized at each contact-tracing step: for each inferred infector’s set of contacts, edge-specific omissions are realized by Bernoulli draws with prescribed $$A_{jk} = \begin{cases} 1, & \text{if there is a true tie }j \to k \ 0, & \text{otherwise} \end{cases}$$3 (layer-dependent omission probabilities). SCO scenarios restrict omission to non-household and non-work layers (e.g., only friend and local-community contacts), while UCO scenarios apply uniform error rates except for a fixed 50% loss in the community layer (Chae et al., 21 Jan 2026).

4. Quantitative Effects of Contact-Omission

The performance implications of CO are dataset and scenario dependent.

• CSS estimation accuracy: Both RTM and Adaptive-Threshold Methods (ATM) exhibit improved similarity to the true network as the sample size $$A_{jk} = \begin{cases} 1, & \text{if there is a true tie }j \to k \ 0, & \text{otherwise} \end{cases}$$4 increases. RTM matches or surpasses ATM in accuracy without requiring ad-hoc parameter choices, robustly balancing CO and CF contributions even as network density and sample size vary. Excessively low false-positive thresholds in ATM lead to excess omission errors; RTM’s weighting reduces this risk (Yenigun et al., 2016).
• Epidemic spread under CO: In Seoul, increasing SCO omission from 0% to 45% approximately doubles mean cumulative infections, shifts peak incidence later, and moderately increases the transmission-network diameter (saturating around $$A_{jk} = \begin{cases} 1, & \text{if there is a true tie }j \to k \ 0, & \text{otherwise} \end{cases}$$5), but does not produce runaway epidemic cascades. Under UCO, peak sizes and delays rise nearly linearly with omission rate, and infection burden always exceeds SCO for the same nominal omission. Crucially, no critical threshold or phase transition is observed for CO: the impact is monotonic and gradual, in contrast to infector-omission scenarios, which exhibit sharp nonlinearities at modest omission rates (Chae et al., 21 Jan 2026).

5. Practical Implications and Policy Significance

RTM enables accurate network estimation from partial CSS samples, addressing nonresponse and cost constraints in fieldwork. In multilevel inter-organizational studies, RTM facilitates efficient inference without complete enumeration, preserving structural fidelity even from modest random samples. Cost-weighted threshold selection adapts estimation for contexts where omission errors are especially deleterious (e.g., terrorist-link detection) or where over-inclusion (excess commissions) entails higher risk (Yenigun et al., 2016).

In epidemic contact tracing, insights from CO simulation indicate that moderate rates of missed contact notification (20–40%) are tolerated without surges in epidemic size or depth, provided case (infector) trajectories are reliably reconstructed. Consequently, prioritizing comprehensive infector investigation yields greater gains than attempting exhaustive edge-level contact tracing. An observed monotonic increase in transmission-network diameter offers a real-time indicator of degraded CT efficacy; thus, monitoring this structural property can inform operational triggers before case surges are apparent (Chae et al., 21 Jan 2026).

6. Comparative Perspectives and Network-Specific Considerations

CO impacts are fundamentally distinct from infector-omission (IO) scenarios. IO, corresponding to node removal and trajectory loss, precipitates abrupt increases in outbreak size and network diameter at low omission rates—essentially unveiling long, hidden chains whose detection would otherwise have severed ongoing transmission. In contrast, CO, whether selective or uniform, produces incremental burden-by-reduction of local containment, but does not fundamentally alter superspreading potential (the out-degree distribution remains fat-tailed under all tested omission intensities). Lower-density or smaller cities (e.g., Busan) exhibit milder amplification in both peak and diameter metrics under equivalent CO, suggesting heterogeneous resilience to information loss across network contexts. This suggests that robust CT system design should align tolerances for CO with spatial network properties and available public-health resources (Chae et al., 21 Jan 2026).

7. Limitations and Directions for Further Research

The context-dependence of CO impacts, especially with respect to real-world respondent behavior in CSS or local heterogeneities in social mixing and CT system performance during epidemics, constrains the generalizability of formal findings. Both frameworks assume accurate assignment of omission probabilities, but empirical estimation of these parameters remains challenging. Further research could systematically address CO in dynamic and directed networks, extend ROC-based thresholding to non-binary edge or weighted networks, and operationalize real-time structural monitoring (e.g., network diameter tracking) as part of adaptive CT deployment strategies. A plausible implication is that combining both node-level (IO) and edge-level (CO) modeling in joint frameworks may be necessary for a full accounting of information loss effects in complex networked systems.