# Technical Data Extraction: Path Length Distributions This document contains a detailed extraction of data from two histograms representing the distribution of path lengths in two different network datasets: **Bitcoin-Alpha** and **Slashdot**. ## 1. General Layout and Components The image consists of two side-by-side subplots, labeled (a) and (b). * **Y-Axis (Common):** "Proportion of Node Pairs (%)" * **X-Axis (Common):** "Path Length" (Discrete integer values from 1 to 7) * **Data Representation:** * **Blue Hatched Bars:** Represent the empirical frequency of node pairs at a specific path length. * **Red Solid Line:** Represents a fitted normal distribution curve (probability density function) over the discrete data. * **Grid:** Both charts feature a dashed gray background grid for value estimation. --- ## 2. Subplot (a): Bitcoin-Alpha ### Metadata * **Title/Label:** (a) Bitcoin-Alpha * **X-Axis Range:** 1 to 7 * **Y-Axis Range:** 0 to 50% ### Trend Analysis The distribution is unimodal and slightly right-skewed. The majority of node pairs have a path length between 3 and 4. The frequency rises sharply from length 2 to 3, peaks between 3 and 4, and tapers off significantly by length 6. ### Data Point Extraction (Estimated) | Path Length (x) | Proportion of Node Pairs (%) (y) | | :--- | :--- | | 1 | ~0.5% | | 2 | ~8% | | 3 | ~40% | | 4 | ~41% | | 5 | ~10% | | 6 | ~1.5% | | 7 | ~0% | ### Curve Characteristics The red curve peaks at approximately **x = 3.5** with a maximum value of roughly **45%**. --- ## 3. Subplot (b): Slashdot ### Metadata * **Title/Label:** (b) Slashdot * **X-Axis Range:** 1 to 7 * **Y-Axis Range:** 0 to 70% (Note: Higher scale than Bitcoin-Alpha) ### Trend Analysis The distribution is highly concentrated (low variance) compared to Bitcoin-Alpha. It is strongly unimodal with a very sharp peak at path length 4. Almost no node pairs exist at path lengths 1, 6, or 7. ### Data Point Extraction (Estimated) | Path Length (x) | Proportion of Node Pairs (%) (y) | | :--- | :--- | | 1 | ~0% | | 2 | ~3% | | 3 | ~25% | | 4 | ~65% | | 5 | ~8% | | 6 | ~0.5% | | 7 | ~0% | ### Curve Characteristics The red curve peaks precisely at **x = 4** with a maximum value of approximately **65%**. The curve is narrower than in the Bitcoin-Alpha plot, indicating a more uniform path length across the network. --- ## 4. Comparative Summary * **Central Tendency:** Both networks exhibit "Small World" properties, with most nodes connected by 3 to 4 hops. * **Concentration:** The **Slashdot** network is more tightly clustered around a path length of 4, whereas **Bitcoin-Alpha** has a more even distribution between lengths 3 and 4. * **Network Reach:** In both datasets, it is extremely rare for node pairs to have a shortest path length greater than 6.