## Box Plot: Average Number of Neighbors vs. Step Number for Different Model Variants ### Overview The image is a box plot comparing the average number of neighbors for three different model variants (Hybrid (LLM), Hybrid (NetLogo), and NetLogo) across various step numbers. The x-axis represents the step number, and the y-axis represents the average number of neighbors. The plot displays the distribution of the average number of neighbors for each model variant at each step number using box plots. ### Components/Axes * **Title:** None explicitly given in the image. * **X-axis:** * Label: "Step Number" * Scale: 0 to 750, with markers at 0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, and 750. * **Y-axis:** * Label: "Average Number of Neighbors" * Scale: 2.5 to 17.5, with markers at 2.5, 5.0, 7.5, 10.0, 12.5, 15.0, and 17.5. * **Legend:** Located in the top-left corner. * Hybrid (LLM): Teal color * Hybrid (NetLogo): Salmon color * NetLogo: Slate Blue color ### Detailed Analysis The data is presented as box plots, where each box represents the interquartile range (IQR), the line inside the box represents the median, the whiskers extend to 1.5 times the IQR, and the circles represent outliers. **Hybrid (LLM) - Teal:** * Trend: Generally increasing from step 0 to step 350, then appears to plateau with some fluctuations. * Step 0: Median around 1 * Step 50: Median around 2 * Step 100: Median around 3 * Step 150: Median around 4.5 * Step 200: Median around 5 * Step 250: Median around 6 * Step 300: Median around 7 * Step 350: Median around 5.5 * Step 400: Median around 2.5 * Step 450: Median around 7 * Step 500: Median around 7 * Step 550: Median around 9 * Step 600: Median around 9 * Step 650: Median around 9 * Step 700: Median around 9 * Step 750: Median around 9 **Hybrid (NetLogo) - Salmon:** * Trend: Generally increasing from step 50 to step 750. * Step 50: Median around 2.5 * Step 100: Median around 3.5 * Step 150: Median around 5 * Step 200: Median around 5.5 * Step 250: Median around 7 * Step 300: Median around 7 * Step 350: Median around 8 * Step 400: Median around 10 * Step 450: Median around 9 * Step 500: Median around 8 * Step 550: Median around 10 * Step 600: Median around 12 * Step 650: Median around 12 * Step 700: Median around 11 * Step 750: Median around 12 **NetLogo - Slate Blue:** * Trend: Generally increasing from step 50 to step 750. * Step 50: Median around 2 * Step 100: Median around 2 * Step 150: Median around 3.5 * Step 200: Median around 5 * Step 250: Median around 7 * Step 300: Median around 8 * Step 350: Median around 9 * Step 400: Median around 12 * Step 450: Median around 12 * Step 500: Median around 11 * Step 550: Median around 12 * Step 600: Median around 14 * Step 650: Median around 15 * Step 700: Median around 15 * Step 750: Median around 15 ### Key Observations * The Hybrid (LLM) model shows an initial increase in the average number of neighbors, but plateaus after step 350. * The Hybrid (NetLogo) and NetLogo models show a consistent increase in the average number of neighbors as the step number increases. * The NetLogo model generally has a higher average number of neighbors compared to the other two models, especially at later steps. * There are several outliers in all three models, indicating some variability in the average number of neighbors. ### Interpretation The box plot suggests that the NetLogo model and the Hybrid (NetLogo) model tend to form more connections (neighbors) as the simulation progresses, while the Hybrid (LLM) model's connectivity plateaus. This could indicate that the NetLogo and Hybrid (NetLogo) models are more effective at establishing and maintaining connections within the simulation environment as the number of steps increases. The Hybrid (LLM) model might have a different mechanism that limits the number of neighbors it forms after a certain point. The outliers suggest that there are instances where the average number of neighbors deviates significantly from the typical range for each model at each step. This could be due to random variations in the simulation or specific conditions that cause some agents to have significantly more or fewer neighbors than usual.

## Box Plot: Average Number of Neighbors vs. Step Number for Different Model Variants ### Overview The image presents a box plot comparing the average number of neighbors for three different model variants – Hybrid (LLM), Hybrid (NetLogo), and NetLogo – across 750 steps. The plot visualizes the distribution of the average number of neighbors at each step, showing the median, quartiles, and outliers. ### Components/Axes * **X-axis:** Step Number (ranging from 0 to 750, with increments of approximately 50). * **Y-axis:** Average Number of Neighbors (ranging from 0 to 17.5, with increments of approximately 2.5). * **Legend:** Located in the top-right corner, identifying the model variants and their corresponding colors: * Hybrid (LLM) - Teal/Green * Hybrid (NetLogo) - Orange/Brown * NetLogo - Gray/Light Blue * **Data Representation:** Box plots with whiskers extending to 1.5 times the interquartile range (IQR). Outliers are represented as individual circles. ### Detailed Analysis The data is presented as a series of box plots, one for each model variant at each step number. I will analyze each model variant's trend and then extract approximate data points. **Hybrid (LLM) - Teal/Green:** The trend for Hybrid (LLM) is generally upward, with a significant increase in the average number of neighbors between steps 0-250, followed by a plateau and some fluctuations between steps 250-750. * Step 0: Median ≈ 2.0, IQR ≈ 0.5 - 2.5 * Step 50: Median ≈ 2.5, IQR ≈ 2.0 - 3.0 * Step 100: Median ≈ 3.0, IQR ≈ 2.5 - 4.0 * Step 150: Median ≈ 4.0, IQR ≈ 3.0 - 5.0 * Step 200: Median ≈ 5.0, IQR ≈ 4.0 - 6.0 * Step 250: Median ≈ 6.0, IQR ≈ 5.0 - 7.0 * Step 300: Median ≈ 7.0, IQR ≈ 6.0 - 8.0 * Step 350: Median ≈ 8.5, IQR ≈ 7.0 - 10.0 * Step 400: Median ≈ 9.0, IQR ≈ 7.5 - 11.0 * Step 450: Median ≈ 9.5, IQR ≈ 8.0 - 12.0 * Step 500: Median ≈ 9.0, IQR ≈ 7.5 - 11.5 * Step 550: Median ≈ 10.0, IQR ≈ 8.5 - 12.5 * Step 600: Median ≈ 11.0, IQR ≈ 9.0 - 13.0 * Step 650: Median ≈ 12.0, IQR ≈ 10.0 - 14.0 * Step 700: Median ≈ 12.5, IQR ≈ 10.5 - 15.0 * Step 750: Median ≈ 12.0, IQR ≈ 10.0 - 14.5 **Hybrid (NetLogo) - Orange/Brown:** The trend for Hybrid (NetLogo) shows a rapid increase from steps 0-250, followed by a more gradual increase and stabilization between steps 250-750. * Step 0: Median ≈ 2.0, IQR ≈ 1.5 - 2.5 * Step 50: Median ≈ 2.5, IQR ≈ 2.0 - 3.0 * Step 100: Median ≈ 3.5, IQR ≈ 2.5 - 4.5 * Step 150: Median ≈ 4.5, IQR ≈ 3.5 - 5.5 * Step 200: Median ≈ 5.5, IQR ≈ 4.5 - 7.0 * Step 250: Median ≈ 6.5, IQR ≈ 5.5 - 8.0 * Step 300: Median ≈ 7.5, IQR ≈ 6.5 - 9.0 * Step 350: Median ≈ 8.5, IQR ≈ 7.0 - 10.0 * Step 400: Median ≈ 9.5, IQR ≈ 8.0 - 11.0 * Step 450: Median ≈ 10.0, IQR ≈ 8.5 - 12.0 * Step 500: Median ≈ 9.5, IQR ≈ 8.0 - 11.5 * Step 550: Median ≈ 10.5, IQR ≈ 9.0 - 12.5 * Step 600: Median ≈ 12.0, IQR ≈ 10.0 - 14.0 * Step 650: Median ≈ 12.5, IQR ≈ 10.5 - 14.5 * Step 700: Median ≈ 13.0, IQR ≈ 11.0 - 15.0 * Step 750: Median ≈ 12.0, IQR ≈ 10.0 - 14.0 **NetLogo - Gray/Light Blue:** The trend for NetLogo is similar to Hybrid (NetLogo), with a rapid increase from steps 0-250, followed by a more gradual increase and stabilization between steps 250-750. * Step 0: Median ≈ 2.0, IQR ≈ 1.5 - 2.5 * Step 50: Median ≈ 2.5, IQR ≈ 2.0 - 3.0 * Step 100: Median ≈ 3.5, IQR ≈ 2.5 - 4.5 * Step 150: Median ≈ 4.5, IQR ≈ 3.5 - 5.5 * Step 200: Median ≈ 5.5, IQR ≈ 4.5 - 7.0 * Step 250: Median ≈ 6.5, IQR ≈ 5.5 - 8.0 * Step 300: Median ≈ 7.5, IQR ≈ 6.5 - 9.0 * Step 350: Median ≈ 8.5, IQR ≈ 7.0 - 10.0 * Step 400: Median ≈ 9.5, IQR ≈ 8.0 - 11.0 * Step 450: Median ≈ 10.0, IQR ≈ 8.5 - 12.0 * Step 500: Median ≈ 9.5, IQR ≈ 8.0 - 11.5 * Step 550: Median ≈ 10.5, IQR ≈ 9.0 - 12.5 * Step 600: Median ≈ 12.0, IQR ≈ 10.0 - 14.0 * Step 650: Median ≈ 12.5, IQR ≈ 10.5 - 14.5 * Step 700: Median ≈ 13.0, IQR ≈ 11.0 - 15.0 * Step 750: Median ≈ 12.0, IQR ≈ 10.0 - 14.0 ### Key Observations * All three model variants exhibit a similar initial increase in the average number of neighbors. * Hybrid (LLM) generally has a lower average number of neighbors compared to the other two variants, especially in the initial steps. * Hybrid (NetLogo) and NetLogo show very similar trends and values throughout the 750 steps. * Outliers are present in all three model variants, indicating variability in the number of neighbors at each step. ### Interpretation The data suggests that the Hybrid (NetLogo) and NetLogo models are more effective at establishing connections (neighbors) than the Hybrid (LLM) model, particularly in the early stages of the simulation. The similar performance of Hybrid (NetLogo) and NetLogo indicates that the underlying NetLogo component is a significant driver of neighbor establishment. The increasing trend in the average number of neighbors across all models suggests that the system is becoming more interconnected over time. The presence of outliers indicates that there is some degree of randomness or variability in the neighbor establishment process. The plateauing of the average number of neighbors after step 250 suggests that the system is approaching a saturation point, where further increases in connectivity become more difficult. This could be due to limitations in the network structure or the dynamics of the simulation. Further investigation would be needed to understand the specific factors driving these trends and the implications for the overall system behavior.

## Box Plot Chart: Average Number of Neighbors by Model Variant Over Simulation Steps ### Overview This image is a box plot chart comparing the distribution of the "Average Number of Neighbors" across three different model variants at discrete simulation step intervals. The chart tracks how this metric evolves from step 0 to step 750. ### Components/Axes * **Chart Type:** Grouped Box Plot. * **X-Axis:** Labeled **"Step Number"**. It represents discrete time steps in a simulation, with major tick marks at intervals of 50, ranging from 0 to 750. * **Y-Axis:** Labeled **"Average Number of Neighbors"**. It represents a quantitative metric, with a scale from 0 to 17.5, marked at intervals of 2.5. * **Legend:** Located in the **top-left corner** of the chart area. It defines the three data series by color: * **Green (Teal):** `Hybrid (LLM)` * **Orange (Salmon):** `Hybrid (NetLogo)` * **Blue (Periwinkle):** `NetLogo` * **Data Representation:** For each step number (0, 50, 100, ..., 750), three box plots are displayed side-by-side, one for each model variant, following the color scheme from the legend. Each box plot shows the median (central line), interquartile range (the box), whiskers (extending to 1.5x the IQR), and individual outlier points (circles). ### Detailed Analysis The analysis is segmented by model variant, describing the visual trend before extracting approximate data points. **1. Hybrid (LLM) - Green/Teal Boxes** * **Trend:** Shows a general upward trend but with extremely high variability (very tall boxes and long whiskers) starting from around step 300. The median increases slowly. * **Approximate Data Points (Median):** * Step 0: ~1.5 * Step 50: ~2.0 * Step 100: ~3.0 * Step 150: ~5.0 * Step 200: ~5.0 * Step 250: ~5.5 * Step 300: ~7.0 * Step 350: ~5.5 (Note: Median drops here, but the box spans from ~3 to ~6) * Step 400: ~6.5 * Step 450: ~7.0 * Step 500: ~7.5 * Step 550: ~6.5 * Step 600: ~5.5 * Step 650: ~7.0 * Step 700: ~7.0 * Step 750: ~9.0 * **Variability:** From step 350 onward, the interquartile range (box height) is very large, often spanning 4-6 units on the y-axis. Whiskers frequently extend from below 2.5 to above 10.0. **2. Hybrid (NetLogo) - Orange/Salmon Boxes** * **Trend:** Shows a steady, consistent upward trend with moderate variability. The median increases more reliably than the LLM hybrid. * **Approximate Data Points (Median):** * Step 0: ~1.5 * Step 50: ~2.5 * Step 100: ~3.0 * Step 150: ~5.0 * Step 200: ~5.5 * Step 250: ~7.0 * Step 300: ~7.5 * Step 350: ~7.5 * Step 400: ~8.5 * Step 450: ~9.0 * Step 500: ~8.5 * Step 550: ~10.0 * Step 600: ~10.5 * Step 650: ~10.0 * Step 700: ~9.5 * Step 750: ~12.0 * **Variability:** The boxes are generally shorter than the LLM hybrid, indicating less spread in the middle 50% of the data. Whiskers are also shorter. **3. NetLogo - Blue/Periwinkle Boxes** * **Trend:** Shows the strongest and most consistent upward trend, achieving the highest median values by the end of the simulation. Variability is moderate. * **Approximate Data Points (Median):** * Step 0: ~1.5 * Step 50: ~2.0 * Step 100: ~3.5 * Step 150: ~4.5 * Step 200: ~6.0 * Step 250: ~6.5 * Step 300: ~7.0 * Step 350: ~9.5 * Step 400: ~10.0 * Step 450: ~13.0 * Step 500: ~12.0 * Step 550: ~12.5 * Step 600: ~14.5 * Step 650: ~14.5 * Step 700: ~14.0 * Step 750: ~14.0 * **Variability:** The interquartile ranges are relatively consistent. The highest single outlier point on the chart (a circle near y=17.5) belongs to this series at step 600. ### Key Observations 1. **Diverging Performance:** All models start similarly at step 0 (median ~1.5). By step 750, their median values have diverged significantly: NetLogo (~14.0) > Hybrid (NetLogo) (~12.0) > Hybrid (LLM) (~9.0). 2. **Variability Contrast:** The `Hybrid (LLM)` model exhibits dramatically higher variance (taller boxes, longer whiskers) from step 350 onward compared to the other two models. Its performance is much less predictable. 3. **NetLogo Dominance:** The pure `NetLogo` model consistently achieves the highest median "Average Number of Neighbors" from approximately step 350 onward. 4. **Outliers:** Outlier points (circles) are present for all models across many steps, indicating occasional simulation runs that produced results far from the central distribution. 5. **Step 350 Anomaly:** At step 350, the median for `Hybrid (LLM)` drops noticeably compared to its trend, while the other two models continue their upward trajectory. ### Interpretation The data suggests a clear hierarchy in the models' ability to generate or maintain neighbor connections over time in this simulation. The pure `NetLogo` model is the most effective and consistent at increasing the average number of neighbors. The `Hybrid (NetLogo)` model performs well, following a similar but slightly lower trajectory. The `Hybrid (LLM)` model, while showing an overall increase, is characterized by high instability and lower final performance. This could imply that integrating a Large Language Model (LLM) into the hybrid system introduces significant noise or unpredictability into the agent behavior governing neighbor relationships, whereas the rule-based NetLogo environment produces more stable and scalable outcomes for this specific metric. The high variance in the LLM hybrid might be a critical finding, suggesting it requires further tuning or that its decision-making process leads to a wider range of emergent social structures. The chart effectively demonstrates not just the central tendency but the crucial difference in reliability between the modeling approaches.

## Box Plot: Average Number of Neighbors by Model Variant and Step Number ### Overview The image displays a comparative box plot analysis of three model variants (Hybrid LLM, Hybrid NetLogo, and NetLogo) across incremental step numbers (0–750). The y-axis represents the average number of neighbors, while the x-axis tracks step progression. Each model variant is represented by distinct colors: green (Hybrid LLM), orange (Hybrid NetLogo), and blue (NetLogo). Outliers are marked as individual dots beyond the whiskers. ### Components/Axes - **Title**: "Model Variant" (legend header) - **X-axis**: "Step Number" (0–750, linear scale) - **Y-axis**: "Average Number of Neighbors" (0–17.5, linear scale) - **Legend**: Top-left corner, mapping colors to model variants: - Green: Hybrid (LLM) - Orange: Hybrid (NetLogo) - Blue: NetLogo - **Box Plot Elements**: - Median line (bold horizontal line within each box) - Interquartile range (IQR, box height) - Whiskers (extending to 1.5×IQR) - Outliers (dots beyond whiskers) ### Detailed Analysis 1. **Step 0–100**: - All models show low median values (1–3 neighbors). - Hybrid LLM (green) has the lowest median (~2), while NetLogo (blue) has the highest (~3). - Minimal variability (narrow boxes and few outliers). 2. **Step 100–300**: - Gradual increase in medians: - Hybrid LLM: ~4–6 - Hybrid NetLogo: ~5–7 - NetLogo: ~6–8 - Box plots widen, indicating increased variability. - Outliers begin appearing (~7–10 neighbors). 3. **Step 300–500**: - Medians rise sharply: - Hybrid LLM: ~8–10 - Hybrid NetLogo: ~9–11 - NetLogo: ~11–13 - Outliers extend to ~14–16 neighbors. - Hybrid LLM surpasses Hybrid NetLogo in median values. 4. **Step 500–750**: - Medians plateau but remain elevated: - Hybrid LLM: ~10–12 - Hybrid NetLogo: ~12–14 - NetLogo: ~14–16 - Box plots are widest, showing high variability. - Outliers reach up to ~18 neighbors (NetLogo). ### Key Observations - **Trend**: All models exhibit increasing medians with step progression, with NetLogo consistently outperforming others. - **Outliers**: More frequent in later steps, suggesting rare but extreme outcomes. - **Variability**: Widening boxes at higher steps indicate greater divergence in neighbor counts. - **Color Consistency**: Legend colors match box plot hues (green/orange/blue) without discrepancies. ### Interpretation The data demonstrates that **NetLogo** maintains the highest average neighbor count across all steps, while **Hybrid LLM** shows the most significant improvement over time, overtaking Hybrid NetLogo by step 500. The increasing variability in later steps suggests that model performance becomes less predictable as steps progress. Outliers in advanced steps may indicate edge cases or anomalies in neighbor distribution. This trend could reflect differences in model architecture, optimization strategies, or sensitivity to incremental changes in input data.