From raw Wikipedia data to predictive intelligence — a complete knowledge graph pipeline that reveals the hidden structure of nanotechnology research.
Beginner
Professional
Technical
📚
Wikipedia
Data Source
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📸
Snapshots
2020–2026
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🕸️
Graph Build
Nodes & Edges
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📊
Analytics
PageRank · Centrality
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🤖
ML Model
XGBoost
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🔮
Predictions
2027 Forecast
📐 Metrics Reference
Every node in the knowledge graph is scored on 16 dimensions. Here are the key metrics that power the analysis and predictions.
📈
PageRank
Measures a topic's global influence — how important it is based on how many other important topics link to it. Originally invented by Google to rank web pages. A high PageRank means the topic is widely cited by other influential concepts.
PR(A) = (1-d) + d × Σ PR(Tᵢ)/C(Tᵢ)
🌉
Betweenness Centrality
How often this topic appears on the shortest path between any two other topics. High betweenness means it's a "bridge" connecting different research areas — these nodes are critical for knowledge flow.
CB(v) = Σ σst(v) / σst
🎯
Closeness Centrality
Measures how close a node is to all other nodes. Topics with high closeness can reach any other topic in fewer steps, meaning they're at the center of the knowledge network.
CC(v) = (n-1) / Σ d(v,u)
👑
Eigenvector Centrality
Similar to PageRank but measures influence by considering neighbor quality. A topic linked by many high-scoring topics gets a higher eigenvector score — it's not just who links to you, but how important they are.
x(v) = (1/λ) × Σ A(v,t)·x(t)
🔗
Katz Centrality
Counts all paths leading to a node, with longer paths weighted less via an attenuation factor. Captures influence from distant parts of the network that other metrics might miss.
Katz(v) = Σ αᵏ × (Aᵏ)ᵢ
🔄
HITS (Hub & Authority)
Each node has two scores: Authority (linked TO by hubs) and Hub (links TO authorities). Authorities are expert topics; hubs are survey/overview topics that point to many authorities.
Auth(p) = Σ Hub(q), Hub(p) = Σ Auth(q)
🔺
Clustering Coefficient
Measures how interconnected a topic's neighbors are. High clustering = the topic exists in a tight-knit research cluster. Low clustering = the topic bridges disparate areas.
C(v) = 2T(v) / (deg(v) × (deg(v)-1))
🧱
Core Number (k-core)
The highest k-core a node belongs to — a k-core is a subgraph where every node has at least k connections. Higher core number = deeper in the densely connected core of the network.
max k : v ∈ k-core(G)
🌟
Bridging Score
A composite metric combining betweenness centrality with inverse clustering coefficient. Identifies nodes that bridge communities while NOT being part of a tight cluster — the true interdisciplinary connectors.
BS(v) = Betweenness(v) × (1 - Clustering(v))
👥
Avg Neighbor PageRank
The average influence of a topic's neighbors. A topic surrounded by high-PageRank neighbors is in an influential neighborhood — even if it's not yet highly ranked itself, it may rise.
ANP(v) = (1/deg(v)) × Σ PR(u)
🧩 How Communities Are Computed
Communities are groups of topics that are more densely connected to each other than to the rest of the network. They reveal the natural structure of nanotechnology research.
🕸️
Full Graph
1,621 nodes
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📐
Modularity Optimization
Louvain Algorithm
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🎨
Community Assignment
Color-coded groups
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🏷️
Auto-Labeling
Top category name
The Louvain Algorithm works in two phases that repeat until optimal:
Phase 1 — Local moves: Each node is initially its own community. The algorithm tries moving each node to a neighboring community and checks if this improves modularity (a score from -1 to 1 measuring how well-separated communities are). Moves that increase modularity are kept.
Phase 2 — Aggregation: Each community is collapsed into a single "super-node," creating a smaller graph. Phase 1 repeats on this compressed graph. This continues until modularity can't improve further.
Community names are assigned automatically by finding the most common Wikipedia category among all nodes in each community. For example, a community full of drug delivery, nanomedicine, and biocompatibility articles gets labeled by the dominant shared category.
🤖 Prediction Model Architecture
An XGBoost gradient-boosted tree model trained on 7 years of graph evolution to predict which topics will grow in importance by 2027.
500
Trees (Estimators)
6
Max Tree Depth
0.05
Learning Rate
16
Input Features
~7,500
Training Samples
0.8
Subsample Ratio
How it works: For each node at year t, the model takes 16 graph metrics (PageRank, degree, betweenness, etc.) as input features and predicts that node's PageRank at year t+1. The model is trained on years 2020→2021, 2021→2022, ..., 2025→2026, then applied to 2026 features to forecast 2027.
Model Parameters Explained:
Trees (500): The number of decision trees in the ensemble. More trees allow the model to learn complex patterns.
Max Tree Depth (6): Limits how deep each tree can grow, preventing the model from simply memorizing the training data.
Learning Rate (0.05): The step size during learning. A smaller value ensures steady, robust learning.
Input Features (16): The 16 graph topology metrics used as clues to predict future importance.
Training Samples (~7,500): Total historical node observations used to train the XGBoost algorithm.
Subsample Ratio (0.8): The fraction of data randomly sampled for each tree, which helps prevent overfitting.
Feature Importance (from XGBoost)
How Trend Labels Are Computed
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Rising
Predicted growth > +5%
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Stable
Growth between -5% and +5%
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Declining
Predicted growth < -5%
Confidence scores are derived from the prediction score — higher prediction scores indicate stronger model certainty. A topic with many consistent graph-structural signals (growing degree, rising PageRank, increasing betweenness) receives higher confidence.
Emerging Topics 2027
XGBoost model predictions based on 7 years of knowledge graph evolution