## Bar Chart: Number of Solved Tasks ### Overview The image is a bar chart comparing the number of solved tasks across different configurations (Neo4j, NetworkX, Neo4j + NetworkX, and No KG) and task types (Query, Direct Retrieve, Query + DR, Single Run #1, Single Run #2, Fusion). The chart displays the number of solved tasks, broken down into three levels (Level 1, Level 2, and Level 3). ### Components/Axes * **Title:** Number of Solved Tasks (the higher the better) * **Y-axis:** Number of Solved Tasks (the higher the better), ranging from 0 to 80. * **X-axis:** Task types: Query, Direct Retrieve, Query + DR, Single Run #1, Single Run #2, Fusion. These are grouped under the configurations Neo4j, NetworkX, Neo4j + NetworkX, and No KG. * **Legend:** Located at the top of the chart. * Level 1: Light Blue * Level 2: Blue * Level 3: Purple * **Horizontal Dashed Line:** At y=71, labeled "Max: 71" ### Detailed Analysis **Neo4j** * **Query:** * Level 1: 21 * Level 2: 18 * Level 3: 1 * **Direct Retrieve:** * Level 1: 21 * Level 2: 16 * Level 3: 3 * **Query + DR:** * Level 1: 29 * Level 2: 24 * Level 3: 4 **NetworkX** * **Query:** * Level 1: 20 * Level 2: 21 * Level 3: 2 * **Direct Retrieve:** * Level 1: 20 * Level 2: 18 * Level 3: 2 * **Query + DR:** * Level 1: 27 * Level 2: 28 * Level 3: 2 **Neo4j + NetworkX** * **Query:** * Level 1: 28 * Level 2: 25 * Level 3: 3 * **Direct Retrieve:** * Level 1: 26 * Level 2: 24 * Level 3: 3 * **Query + DR:** * Level 1: 34 * Level 2: 33 * Level 3: 4 **No KG** * **Single Run #1:** * Level 1: 14 * Level 2: 14 * Level 3: 2 * **Single Run #2:** * Level 1: 17 * Level 2: 16 * Level 3: 2 * **Fusion:** * Level 1: 18 * Level 2: 20 * Level 3: 2 ### Key Observations * The "Query + DR" task in the "Neo4j + NetworkX" configuration achieves the highest number of solved tasks. * The "No KG" configuration generally has lower numbers of solved tasks compared to the other configurations. * Level 1 and Level 2 contribute the most to the total number of solved tasks, with Level 3 contributing the least. ### Interpretation The chart demonstrates the performance of different knowledge graph systems (Neo4j, NetworkX, and their combination) on various tasks. The "Neo4j + NetworkX" configuration appears to be the most effective, particularly for the "Query + DR" task. The "No KG" configuration serves as a baseline, showing the performance without a knowledge graph. The breakdown into levels could represent different difficulty levels or types of tasks, with Level 1 and Level 2 being more frequently solved than Level 3. The horizontal line at 71 indicates a maximum possible score, suggesting that the "Neo4j + NetworkX" configuration is approaching the optimal performance for the "Query + DR" task.

\n ## Bar Chart: Performance Comparison of Knowledge Graph Systems ### Overview This bar chart compares the performance of different knowledge graph systems (Neo4j, NetworkX, and combinations thereof) across various approaches (Direct Retrieve, Query, Query + DR) and levels of task complexity (Level 1, Level 2, Level 3). The performance metric is the "Number of Solved Tasks," where a higher number indicates better performance. A "Max" value is also indicated. ### Components/Axes * **X-axis:** Represents the different system configurations and approaches. Categories are: "Direct Retrieve", "Query", "Query + DR", "Single Run #1", "Single Run #2", "Fusion". These are further grouped under "Neo4j", "NetworkX", "Neo4j + NetworkX", and "No KG". * **Y-axis:** Represents the "Number of Solved Tasks" with a scale from 0 to 80. The label also states "(the higher the better)". * **Legend:** * Level 1: Light Blue * Level 2: Medium Blue * Level 3: Purple * Max: Grey * **Title:** Not explicitly present, but the chart's content implies a title related to performance comparison. ### Detailed Analysis The chart consists of grouped bar plots for each system configuration. Each group has three bars representing Level 1, Level 2, and Level 3 tasks, plus a grey "Max" bar. **Neo4j:** * **Direct Retrieve:** Level 1: ~21, Level 2: ~18, Level 3: ~16 * **Query:** Level 1: ~40, Level 2: ~21, Level 3: ~21 * **Query + DR:** Level 1: ~24, Level 2: ~29, Level 3: ~42 **NetworkX:** * **Direct Retrieve:** Level 1: ~20, Level 2: ~20, Level 3: ~18 * **Query:** Level 1: ~28, Level 2: ~21, Level 3: ~28 * **Query + DR:** Level 1: ~60, Level 2: ~34, Level 3: ~2 **Neo4j + NetworkX:** * **Direct Retrieve:** Level 1: ~25, Level 2: ~26, Level 3: ~24 * **Query:** Level 1: ~54, Level 2: ~33, Level 3: ~3 * **Query + DR:** Level 1: ~72, Level 2: ~33, Level 3: ~5 **No KG:** * **Single Run #1:** Level 1: ~14, Level 2: ~14, Level 3: ~2 * **Single Run #2:** Level 1: ~20, Level 2: ~16, Level 3: ~18 * **Fusion:** Level 1: ~32, Level 2: ~42, Level 3: ~38 ### Key Observations * The "Query + DR" approach generally performs best for Neo4j and Neo4j + NetworkX, especially at Level 1. * NetworkX shows a significant performance boost with the "Query + DR" approach at Level 1, outperforming Neo4j and Neo4j + NetworkX. * Level 3 tasks consistently have the lowest solved counts across all configurations. * The "Max" value is relatively low across all configurations, suggesting a ceiling on performance. * The "Fusion" approach in the "No KG" category shows the highest performance among the "No KG" configurations. ### Interpretation The chart demonstrates the effectiveness of combining query-based and direct retrieval approaches for knowledge graph systems. The "Query + DR" strategy appears to leverage the strengths of both methods, leading to improved performance, particularly for Level 1 tasks. The performance differences between Neo4j, NetworkX, and their combination suggest that each system has unique capabilities and limitations. The consistently low performance on Level 3 tasks indicates that these tasks are inherently more challenging or require more sophisticated reasoning capabilities than the systems currently possess. The "Max" value suggests that there is a limit to the number of tasks that can be solved, even with the best configuration. The "No KG" category provides a baseline for comparison, and the "Fusion" approach shows that even without a dedicated knowledge graph, reasonable performance can be achieved through alternative methods. The chart highlights the importance of selecting the appropriate system configuration and approach based on the specific task complexity and desired performance level.

## Grouped Bar Chart: Knowledge Graph System Performance on Task Solving ### Overview The image is a grouped, stacked bar chart comparing the performance of four different knowledge graph (KG) systems or configurations across three distinct task types. Performance is measured by the number of solved tasks, with a higher number being better. The chart includes a maximum performance benchmark line. ### Components/Axes * **Chart Type:** Grouped, stacked bar chart. * **Y-Axis:** Labeled "Number of Solved Tasks (the higher the better)". Scale ranges from 0 to 80, with major gridlines at intervals of 10. * **X-Axis:** Categorical, showing four main system groups, each containing three task types. * **Main System Groups (from left to right):** `Neo4j`, `NetworkX`, `Neo4j + NetworkX`, `No KG`. * **Task Types within each group (from left to right):** `Query`, `Direct Retrieve`, `Query + DR`. * **Legend:** Positioned at the top-center of the chart area. Defines three performance levels represented by stacked bar segments: * `Level 1` (Light Cyan/Teal) * `Level 2` (Medium Blue) * `Level 3` (Dark Blue/Purple) * **Benchmark Line:** A horizontal dashed gray line near the top of the chart, labeled "Max: 71" on the right side, indicating a maximum possible or target score. ### Detailed Analysis The chart presents numerical results for each system and task combination, broken down by level. Values are read from the labels on each bar segment. **1. Neo4j System Group (Leftmost)** * **Query Task:** Level 1 = 21, Level 2 = 18, Level 3 = 1. **Total = 40.** * **Direct Retrieve Task:** Level 1 = 21, Level 2 = 16, Level 3 = 3. **Total = 40.** * **Query + DR Task:** Level 1 = 20, Level 2 = 24, Level 3 = 4. **Total = 48.** **2. NetworkX System Group (Second from left)** * **Query Task:** Level 1 = 20, Level 2 = 21, Level 3 = 1. **Total = 42.** * **Direct Retrieve Task:** Level 1 = 20, Level 2 = 18, Level 3 = 2. **Total = 40.** * **Query + DR Task:** Level 1 = 27, Level 2 = 28, Level 3 = 2. **Total = 57.** **3. Neo4j + NetworkX System Group (Third from left)** * **Query Task:** Level 1 = 20, Level 2 = 25, Level 3 = 1. **Total = 46.** * **Direct Retrieve Task:** Level 1 = 26, Level 2 = 24, Level 3 = 3. **Total = 53.** * **Query + DR Task:** Level 1 = 34, Level 2 = 31, Level 3 = 6. **Total = 71.** (This bar reaches the "Max: 71" benchmark line). **4. No KG System Group (Rightmost)** * **Single Run #1 Task:** Level 1 = 14, Level 2 = 14, Level 3 = 1. **Total = 29.** * **Single Run #2 Task:** Level 1 = 17, Level 2 = 16, Level 3 = 0. **Total = 33.** * **Fusion Task:** Level 1 = 19, Level 2 = 20, Level 3 = 2. **Total = 41.** ### Key Observations 1. **Performance Hierarchy:** The combined `Neo4j + NetworkX` system consistently outperforms the individual systems (`Neo4j` and `NetworkX`) and the `No KG` baseline across all comparable tasks. 2. **Task Difficulty:** For all systems with a KG, the `Query + DR` task yields the highest total solved tasks, followed by `Query`, with `Direct Retrieve` generally being the lowest or tied. This suggests the combined task is either easier or better supported by these systems. 3. **Benchmark Achievement:** Only one configuration, `Neo4j + NetworkX` on the `Query + DR` task, achieves the maximum benchmark score of 71. 4. **Level Contribution:** `Level 1` and `Level 2` contribute the vast majority of solved tasks across all systems. `Level 3` contributions are minimal (typically 0-6 tasks), indicating these are the most difficult problems. 5. **No KG Baseline:** The `No KG` system shows the lowest performance, as expected. Its task labels (`Single Run #1`, `Single Run #2`, `Fusion`) differ from the others, suggesting a different experimental setup or capability set. Its best performance (`Fusion`, 41) is comparable to the worst performance of the KG-enabled systems. ### Interpretation This chart demonstrates the significant value of integrating knowledge graph technologies (`Neo4j`, `NetworkX`) for solving complex tasks compared to a system without a structured knowledge base (`No KG`). The data suggests a synergistic effect when combining two different KG technologies (`Neo4j + NetworkX`), as this configuration achieves the highest performance, reaching the predefined maximum benchmark. The consistent pattern where `Query + DR` outperforms standalone `Query` or `Direct Retrieve` tasks implies that the systems benefit from combining retrieval and querying capabilities. The very low contribution of `Level 3` across the board highlights a common challenge or ceiling in solving the most advanced tier of problems, regardless of the underlying system. The experiment likely aims to validate the hypothesis that a hybrid KG architecture provides superior problem-solving capability, which the results strongly support. The `No KG` results serve as a crucial control, quantifying the baseline performance achievable without the structured knowledge representation and reasoning that KGs provide.

## Bar Chart: Performance of Different Methods Across Knowledge Graph Levels ### Overview The chart compares the number of solved tasks across different methods (Neo4j, NetworkX, Neo4j + NetworkX, No KG) and knowledge graph (KG) levels (Level 1, Level 2, Level 3). The y-axis represents the number of solved tasks, with higher values indicating better performance. The x-axis categorizes methods and their configurations, including "Query," "Direct Retrieve," "Query + DR," "Single Run #1," "Single Run #2," and "Fusion." The legend distinguishes the three KG levels by color: cyan (Level 1), blue (Level 2), and purple (Level 3). The maximum value on the y-axis is 71, marked by a dashed line. ### Components/Axes - **X-axis**: Categories of methods and configurations: - Neo4j - NetworkX - Neo4j + NetworkX - No KG - Subcategories: Query, Direct Retrieve, Query + DR, Single Run #1, Single Run #2, Fusion - **Y-axis**: Number of solved tasks (0–80), with a dashed line at 71. - **Legend**: - Level 1 (cyan) - Level 2 (blue) - Level 3 (purple) - **Axis Titles**: - Y-axis: "Number of Solved Tasks (the higher the better)" - X-axis: Method/Configuration labels ### Detailed Analysis - **Neo4j**: - Query: Level 1 (18), Level 2 (16), Level 3 (24) - Direct Retrieve: Level 1 (21), Level 2 (18), Level 3 (29) - Query + DR: Level 1 (21), Level 2 (18), Level 3 (29) - **NetworkX**: - Query: Level 1 (21), Level 2 (18), Level 3 (27) - Direct Retrieve: Level 1 (20), Level 2 (20), Level 3 (27) - Query + DR: Level 1 (28), Level 2 (26), Level 3 (34) - **Neo4j + NetworkX**: - Query: Level 1 (28), Level 2 (26), Level 3 (34) - Direct Retrieve: Level 1 (25), Level 2 (24), Level 3 (33) - Query + DR: Level 1 (28), Level 2 (26), Level 3 (34) - **No KG**: - Single Run #1: Level 1 (14), Level 2 (16), Level 3 (18) - Single Run #2: Level 1 (17), Level 2 (20), Level 3 (20) - Fusion: Level 1 (18), Level 2 (20), Level 3 (20) ### Key Observations 1. **Highest Performance**: - "Query + DR" under "Neo4j + NetworkX" achieves the highest number of solved tasks (34 at Level 3). - "Direct Retrieve" under "Neo4j" also performs well (29 at Level 3). 2. **Lowest Performance**: - "Single Run #1" under "No KG" has the lowest values (14 at Level 1, 16 at Level 2, 18 at Level 3). 3. **Trends**: - "Query + DR" consistently outperforms other configurations across all methods. - "No KG" methods show significantly lower performance compared to others. - Level 3 (purple) bars are generally taller than Level 1 and 2, indicating better performance at higher KG levels. ### Interpretation The data suggests that combining Neo4j and NetworkX (Neo4j + NetworkX) yields the best results, particularly in the "Query + DR" configuration. This implies that integrating multiple knowledge graph systems enhances task-solving capabilities. The "No KG" setup underperforms, highlighting the importance of KG integration. The consistent improvement from Level 1 to Level 3 across methods indicates that higher KG levels correlate with better performance. The "Fusion" method under "No KG" shows moderate improvement but still lags behind KG-integrated approaches. This chart underscores the value of hybrid systems and structured KG levels in optimizing task-solving efficiency.