Authority Graph

Edges in an authority graph are directed and weighted, representing the asymmetric flow of authority from a citing entity to a cited entity. A link from a high-authority node carries more weight than one from a low-authority node. This is the foundational mechanism that distinguishes authority graphs from undirected social graphs.

• Edge weight often derived from citation frequency or contextual relevance
• Directionality prevents reciprocal link schemes from artificially inflating scores
• Weights are continuously updated as new citations or links are discovered

Authority is not monolithic. A single entity can be a domain expert in one topic and a novice in another. Authority graphs partition nodes into topical subgraphs using entity recognition and content classification, ensuring that authority signals remain contextually relevant.

• Nodes are tagged with topic vectors derived from their published content
• Edges are only formed when the citing context matches the cited entity's expertise domain
• Prevents authority leakage where celebrity status in one field incorrectly boosts trust in an unrelated field

Authority graphs require a ground truth seed set of manually vetted, indisputably authoritative nodes to bootstrap the scoring process. These seeds act as the origin points from which trust propagates outward through the graph structure.

• Seeds are selected by domain experts through rigorous curation
• Typically includes peer-reviewed journals, government databases, and established institutions
• The Trust Rank algorithm formalizes this by biasing random walks to start from seed nodes

Authority flows transitively through the graph. If node A cites node B, and node B cites node C, a fraction of A's authority is conferred to C. This propagation depth is carefully controlled to prevent dilution and ensure that authority attenuates with distance from the seed set.

• Propagation follows Markov chain principles with a damping factor
• Typical damping factor is 0.85, meaning 15% of authority is reserved for random discovery
• Attenuation prevents authority farms where distant nodes benefit from long citation chains

Authority is time-sensitive. An entity that was highly cited a decade ago but has produced no recent work should not retain its full authority score. Authority graphs integrate reputation decay functions that systematically reduce edge weights based on the age of the citation.

• Decay functions can be exponential, linear, or step-based
• Recent citations carry higher weight, rewarding active expertise
• Prevents legacy entrenchment where outdated sources dominate search results indefinitely

Authority graphs are engineered to resist manipulation. Link farms, reciprocal citation rings, and citation cartels are detected through graph topology analysis. Sudden, unnatural spikes in edge formation trigger anomaly detection algorithms that quarantine suspicious nodes.

• Clique detection identifies tightly interconnected groups that may be colluding
• Velocity checks flag nodes that accumulate citations at statistically impossible rates
• Penalized nodes are not removed but have their edge weights down-weighted to near-zero

A directed or undirected data structure where nodes represent entities (domains, authors, institutions) and edges represent explicit trust, endorsement, or citation relationships. Unlike a general knowledge graph that maps semantic facts, a reputation graph specifically encodes the subjective or algorithmic assessments of trustworthiness between participants. The edge weight typically quantifies the strength of the endorsement, forming the substrate upon which graph-based trust algorithms like TrustRank and Bayesian Trust Networks operate.

The algorithmic mechanism by which a trust score is transitively assigned from a known, high-authority node to connected or cited entities within an authority graph. Propagation follows the graph's edge direction: if node A trusts node B, and node B cites node C, a fraction of A's trust flows to C. Key considerations include:

• Attenuation factors that reduce trust with each hop
• Cycle detection to prevent infinite loops
• Damping mechanisms to avoid over-concentration on hub nodes

A specific link-analysis algorithm adapted from PageRank that computes trust scores by biasing the random walk to start from a seed set of manually vetted, highly trustworthy nodes. The algorithm assumes that trustworthy pages rarely link to spam, creating an isolation boundary between good and bad actors. Key properties:

• Seed selection quality directly determines output accuracy
• Inverse Trust Rank can identify spam by reversing the propagation direction
• Converges to a stationary distribution after iterative computation

A mathematical array representing the pairwise trust relationships between all entities in a system, used as the adjacency input for linear algebra-based trust propagation and inference. Each cell M[i][j] encodes the trust score that entity i assigns to entity j, typically normalized to a 0–1 range. The matrix enables:

• Eigenvalue decomposition to find stable trust distributions
• Matrix multiplication for multi-hop propagation
• Sparsity optimization for large-scale graphs with millions of nodes

The algorithmic process of predicting an unknown trust relationship between two entities by analyzing the structure of the known trust graph and applying transitive propagation rules. Common approaches include:

• Path-based inference: aggregating trust along all connecting paths
• Similarity-based inference: assuming entities with similar trust profiles trust each other
• Matrix factorization: latent factor models that predict missing entries in the trust matrix This is critical for cold-start scenarios where direct trust data is sparse.

A time-dependent mathematical formula that systematically reduces the weight of older trust signals to prevent stale or outdated authority from indefinitely influencing a current trust score. Common implementations include:

• Exponential decay: weight = e^(-λt) where λ controls the decay rate
• Linear decay: weight = max(0, 1 - t/T) for a fixed window T
• Step functions: discrete drops after predefined time thresholds Without decay, once-authoritative sources that have since become compromised retain unwarranted influence.