## 3 Dataset and Features
### Real Data Collection  
Our initial investigation used real data from Reddit threads [27; 28]. These online discussion networks provided valuable data on information propagation patterns. We collected data from eight unique networks comprising 72 observations in total. This dataset included both discussion and non-discussion threads to capture different interaction dynamics. The Reddit threads in our dataset were selected to represent diverse community types and interaction patterns. We included threads from eight subreddits spanning different topics: technology (r/programming, r/technology), news (r/worldnews), entertainment (r/movies), lifestyle (r/fitness), gaming (r/gaming), science (r/science), and general discussion (r/AskReddit).  
We extracted two key data types from the networks: First, aggregated diffusion results containing spread metrics and parameters. Second, network structural metrics consisting of comprehensive topological features for each network. Both datasets and their processing pipelines are publicly available in our Google Colab repository ([[https://colab.research.google.com/drive/1](https://colab.research.google.com/drive/1) zAxPi7i6 EKtuNqJSdsodpl2J3_Z787m]([https://colab.research.google.com/drive/1](https://colab.research.google.com/drive/1) zAxPi7i6 EKtuNqJSdsodpl2J3_Z787m), accessed on 10 April 2025), enabling the reproducibility and extension of our work.  
The data preparation process involved several cleaning steps. We merged the datasets using the graph_id as the common identifier. This created a combined dataset with 36 features after removing duplicate columns. We handled missing values using median imputation for numeric features when the missing percentage was below 25%. For columns with excessive missing values, such as avg_time_to_half (98.6% missing), we removed them entirely.  
The final dataset included diverse delay types (constant, uniform, exponential) and spread probabilities (0.1, 0.2, 0.3). This variety allowed us to test different information propagation mechanisms. The target variable was avg_coverage, representing the fraction of nodes that received the information.  
Our exploratory analysis revealed several patterns in the real data (Figure 1). The mean coverage across all networks was approximately 0.11 (11%). Discussion threads showed slightly higher coverage (mean difference = 0.033) than non-discussion threads, although this difference was not statistically significant (t = 1.765, \(p\) = 0.082).  
We found no significant differences between delay types (F = 0.172, \(p\) = 0.843). This suggested that the specific delay mechanism may not have strongly influenced the diffusion outcomes in these networks (Figure 2).  
Spread probability showed a significant effect on coverage (F = 12.195, \(p\) < 0.001). Higher spread probabilities consistently led to better information coverage across all network types (Figure 3). A spread probability of 0.3 showed notably higher coverage than 0.1 or 0.2.  
The heatmap visualization (Figure 4) further confirmed that discussion graphs with constant delay achieved the highest average coverage (0.140). This initial finding suggests that transmission probability might be more important than network structure or delay mechanism in determining information spread.  
Figure 1: Distribution of average coverage in real data. The histogram shows frequency distribution, red dashed lines indicate mean (0.110) and median (0.089) values, and the blue curve represents the fitted normal distribution.  
Figure 2: Coverage by graph type and delay type. Box plots show median (center line), quartiles (box boundaries), whiskers (1.5 \(\times\) IQR range), and outliers (circles beyond whiskers).