TextRank

TextRank builds a graph where vertices represent text units (sentences or words) and edges represent co-occurrence within a defined window. For keyword extraction, a window of N words slides across the text, linking all words that appear together. For sentence extraction, edges connect sentences with overlapping lexical content. This unsupervised approach requires no labeled training data, making it domain-agnostic and immediately applicable to any language or corpus.

The algorithm initializes all vertices with a default score of 1 and iteratively updates each vertex's score using the weighted sum of its neighbors' scores until convergence (typically when the change between iterations falls below a threshold of 0.0001). The damping factor—usually set to 0.85—prevents rank sinks and ensures convergence. The final score of a vertex represents its global salience within the entire graph, not just local prominence.

For keyword extraction, TextRank filters candidate words to retain only nouns and adjectives after part-of-speech tagging. Words that are adjacent in the filtered sequence form multi-word keyphrases. The top T vertices by final score are selected as the document's key terms. This variant outperforms TF-IDF on tasks requiring semantic coherence because it captures structural relationships rather than relying solely on raw frequency statistics.

For sentence extraction, TextRank treats each sentence as a vertex and computes edge weights based on content overlap—typically the number of shared lexical tokens normalized by sentence length. This penalizes long sentences that accumulate high overlap purely due to length. The top-ranked sentences are selected in their original order to form an extractive summary, preserving the document's narrative flow without generating new text.

The original TextRank uses undirected, weighted graphs where edge weights are symmetric, reflecting the reciprocal nature of co-occurrence. However, directed variants exist that incorporate forward-looking context—edges point from earlier to later text units within the window—to model the sequential nature of language. Directed graphs can better capture discourse structure but introduce sparsity and require careful tuning of the damping factor to maintain convergence guarantees.

TextRank's primary advantage is its language independence and domain portability. Unlike supervised extractors that require expensive annotated corpora, TextRank operates on raw text alone. It also naturally handles redundancy reduction—the graph-based scoring inherently penalizes duplicate information because vertices that are highly similar to already high-scoring vertices receive diminished marginal contribution, a property analogous to Maximum Marginal Relevance (MMR) without requiring a separate diversity mechanism.

The foundational link analysis algorithm from which TextRank is directly derived. PageRank models the web as a directed graph where pages are nodes and hyperlinks are edges. It computes a recursive importance score based on the principle that a node is important if it is linked to by other important nodes, using a random surfer model with a damping factor (typically 0.85) to prevent rank sinks.

• Formula: PR(A) = (1-d) + d * Σ(PR(Ti)/C(Ti))
• Converges iteratively until scores stabilize
• TextRank adapts this by replacing hyperlinks with lexical co-occurrence edges

A classical bag-of-words weighting scheme that quantifies term importance by multiplying Term Frequency (how often a word appears in a document) by Inverse Document Frequency (how rare the word is across the corpus). Unlike TextRank, TF-IDF is purely statistical and ignores word order, context, and semantic relationships.

• IDF = log(N / df(t))
• Requires a reference corpus for IDF calculation
• TextRank often outperforms TF-IDF for keyphrase extraction because it captures co-occurrence structure rather than raw frequency

A probabilistic relevance ranking function that extends TF-IDF with document length normalization and term frequency saturation. BM25 is the default retrieval algorithm in Elasticsearch and Lucene. While BM25 excels at document ranking for queries, TextRank operates on a single-document graph and identifies salient terms without requiring a query.

• k1 controls term frequency saturation (default 1.2)
• b controls length normalization (default 0.75)
• Both BM25 and TextRank can be combined in hybrid retrieval pipelines

A redundancy-penalizing selection algorithm used in extractive summarization to build a ranked list where each new item balances query relevance against novelty relative to already-selected items. TextRank's sentence extraction can be paired with MMR as a post-processing step to ensure the top-ranked sentences are not repetitive.

• MMR = argmax[λ * Sim(Di, Q) - (1-λ) * max(Sim(Di, Dj))]
• λ parameter controls the relevance-novelty trade-off
• Often applied after TextRank scoring to diversify summaries

The NLP task of automatically identifying the most representative multi-word expressions from a document. TextRank approaches this by building a graph where candidate phrases (filtered by Part-of-Speech patterns) are nodes, and edges connect phrases that co-occur within a sliding window.

• Common POS filter: (JJ)*(NN|NNP|NNS)+
• Alternatives include RAKE (Rapid Automatic Keyword Extraction) and YAKE
• TextRank's graph-based approach captures topical centrality rather than just frequency

A syntactic analysis technique that identifies binary grammatical relations between words in a sentence, producing a directed tree structure. Advanced TextRank variants replace simple co-occurrence windows with dependency-based edges, connecting words that share a syntactic relationship rather than mere proximity.

• Relations include nsubj, dobj, amod, etc.
• Produces sparser, more linguistically meaningful graphs
• Improves precision for entity-centric salience scoring by filtering noise from window-based co-occurrence