Reputation Graph

Edges in a reputation graph are typically directed, capturing the asymmetric nature of trust. An edge from node A to node B signifies that A explicitly endorses, cites, or trusts B. This directionality is critical because trust is not inherently reciprocal—a PhD thesis citing a foundational paper does not imply the paper's author endorses the thesis. Adjacency matrices representing these graphs are therefore asymmetric, and algorithms like Trust Rank exploit this property to propagate scores downstream from seed nodes.

Edges carry weights that quantify the strength of the trust relationship. A weight may represent:

• Citation frequency: How many times entity A has referenced entity B
• Endorsement confidence: A probabilistic score from 0 to 1
• Transaction value: Monetary volume in financial trust networks
• Co-authorship count: Frequency of collaboration Weighted edges enable nuanced propagation where strong endorsements contribute more to a node's accumulated reputation than weak, incidental mentions.

Nodes in a reputation graph are heterogeneous and carry typed attributes that contextualize their role:

• Domain nodes: Represent websites or publishers with attributes like domain age and SSL status
• Author nodes: Individuals with expertise vectors and publication histories
• Content nodes: Articles, papers, or datasets with quality scores
• Organization nodes: Institutions with legal entity identifiers This typing allows context-aware propagation where trust flows differently between an author and their institution versus an author and their published work.

Reputation graphs are time-aware structures. Edges carry timestamps, and the graph evolves as new endorsements form and old ones decay. Key temporal mechanisms include:

• Reputation Decay Functions: Systematically reduce the influence of edges older than a threshold
• Sliding Windows: Only consider edges within a recent timeframe for current trust calculations
• Event Sequencing: Captures the order of endorsements to detect coordinated manipulation patterns Without temporal modeling, a single high-value endorsement from a decade ago could indefinitely prop up a now-compromised entity's trust score.

The core algorithmic value of a reputation graph lies in transitive propagation: if A trusts B, and B trusts C, then A should have some derived trust in C. The amount of trust propagated is governed by:

• Path length: Trust attenuates with each hop, often using a damping factor (e.g., 0.85)
• Path multiplicity: Multiple independent paths from A to C reinforce trust
• Edge weight multiplication: The propagated score is the product of weights along the path This transitivity is what allows algorithms like Trust Rank and Bayesian Trust Networks to infer trust for nodes that have never been directly evaluated.

A well-constructed reputation graph is inherently Sybil-resistant. Malicious actors cannot easily inflate their trust score by creating fake nodes that all endorse each other because:

• Seed set anchoring: Propagation starts from a manually vetted set of high-trust nodes, and Sybil clusters are disconnected from this core
• Conductance boundaries: The graph cut between the legitimate core and a Sybil cluster has low conductance, making the attack mathematically detectable
• Cost imposition: Edge creation may require proof-of-work, stake, or real-world identity verification This structural property makes reputation graphs superior to simple aggregation of unverified ratings.

The algorithmic mechanism by which a trust score is transitively assigned from a known, high-authority entity to connected or cited entities within a reputation graph.

• Uses adjacency matrices to model pairwise relationships
• Applies discount factors to attenuate trust as it traverses multiple hops
• Enables cold-start trust estimation for unvetted nodes based on their neighbors' reputation
• Common in PageRank variants and TrustRank implementations

A 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 random surfer has a higher probability of restarting from trusted seeds
• Effectively demotes spam and low-quality nodes that would otherwise accumulate PageRank
• Seed selection is critical: requires domain experts to curate an irreproachable ground-truth set
• Forms the basis for anti-spam systems in web search and social network analysis

A time-dependent mathematical formula that systematically reduces the weight of older trust signals to prevent stale authority from indefinitely influencing current scores.

• Common implementations: exponential decay, linear decay, step functions
• Half-life parameters define how quickly a signal loses 50% of its weight
• Critical for dynamic environments where entity behavior changes over time
• Prevents reputation lock-in where past achievements permanently dominate

A specialized reputation graph that maps the directional flow of topical authority between entities based on hyperlinks, citations, or co-authorship to identify dominant expert sources.

• Edges represent endorsement: a link from A to B signals A's conferral of authority on B
• Distinguished from social graphs by its focus on expertise rather than friendship
• Used to compute HITS (Hyperlink-Induced Topic Search) authority and hub scores
• Underpins academic citation analysis and expert-finding systems

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.

• Uses path algebra to combine trust values along multiple connecting routes
• Matrix factorization techniques can predict latent trust in sparse graphs
• Handles the cold-start problem where direct trust ratings are unavailable
• Essential for recommender systems and peer-to-peer network security

A probabilistic graphical model that uses Bayesian inference to update an entity's trustworthiness score dynamically as new, potentially uncertain evidence is observed.

• Nodes represent trust variables; edges encode conditional dependencies
• Prior beliefs are updated via Bayes' theorem when new signals arrive
• Naturally handles uncertainty quantification with credible intervals
• Robust to noisy or conflicting signals from multiple reputation sources