RDF [[RDF11-CONCEPTS]] describes a graph-based data model for making claims about the world and provides the foundation for reasoning upon that graph of information. At times, it becomes necessary to compare the differences between sets of graphs, digitally sign them, or generate short identifiers for graphs via hashing algorithms. This document outlines an algorithm for normalizing RDF datasets such that these operations can be performed.

This document describes the RDFC-1.0 algorithm for canonicalizing RDF datasets, which was the input from the W3C Credentials Community Group published as [[CCG-RDC-FINAL]].

At the time of publication, [[RDF11-CONCEPTS]] is the most recent recommendation defining RDF datasets and [[N-QUADS]], however work on an updated specification is ongoing within the W3C RDF-star Working Group. Some dependencies from relevant updated specifications are provided normatively in this specification with the expectation that a future update to this specification will replace those with normative references to updated RDF specifications.

Introduction

When data scientists discuss canonicalization, they do so in the context of achieving a particular set of goals. Since the same information may sometimes be expressed in a variety of different ways, it often becomes necessary to transform each of these different ways into a single, standard representation. With a standard representation, the differences between two different sets of data can be easily determined, a cryptographically-strong hash identifier can be generated for a particular set of data, and a particular set of data may be digitally-signed for later verification.

In particular, this specification is about normalizing RDF datasets, which are collections of graphs. Since a directed graph can express the same information in more than one way, it requires canonicalization to achieve the aforementioned goals and any others that may arise via serendipity.

Most RDF datasets can be canonicalized fairly quickly, in terms of algorithmic time complexity. However, those that contain nodes that do not have globally unique identifiers pose a greater challenge. Normalizing these datasets presents the graph isomorphism problem, a problem that is believed to be difficult to solve quickly in the worst case. Fortunately, existing real world data is rarely, if ever, modeled in a way that manifests as the worst case and new data can be modeled to avoid it. In fact, software systems that detect a problematic dataset (see ) can choose to assume it's an attempted denial of service attack, rather than a real input, and abort.

This document outlines an algorithm for generating a canonical serialization of an RDF dataset given an RDF dataset as input. The algorithm is called the RDF Canonicalization algorithm version 1.0 or RDFC-1.0.

[[[RDF11-CONCEPTS]]] [[RDF11-CONCEPTS]] lacks clarity on the representation of language-tagged strings, where language tags of the form `xx-YY` are treated as being case insensitive. Implementations might represent language tags using all lower case in the form `xx-yy`, retain the original representation `xx-YY`, or use [[BCP47]] formatting conventions, leading to different canonical forms, and therefore, different hashed values.

See for a comparison with the version of the algorithm published in [[[CCG-RDC-FINAL]]] [[CCG-RDC-FINAL]].

Uses of Dataset Canonicalization

There are different use cases where graph or dataset canonicalization are important:

A canonicalization algorithm is necessary, but not necessarily sufficient, to handle many of these use cases. The use of blank nodes in RDF graphs and datasets has a long history and creates inevitable complexities. Blank nodes are used for different purposes:

Furthermore, RDF semantics dictate that deserializing an RDF document results in the creation of unique blank nodes, unless it can be determined that on each occasion, the blank node identifies the same resource. This is due to the fact that blank node identifiers are an aspect of a concrete RDF syntax and are not intended to be persistent or portable. Within the abstract RDF model, blank nodes do not have identifiers (although some RDF store implementations may use stable identifiers and may choose to make them portable). See Blank Nodes in [[RDF11-CONCEPTS]] for more information.

RDF does have a provision for allowing blank nodes to be published in an externally identifiable way through the use of Skolem IRIs, which allow a given RDF store to replace the use of blank nodes in a concrete syntax with IRIs, which then serve to repeatably identify that blank node within that particular RDF store; however, this is not generally useful for talking about the same graph in different RDF stores, or other concrete representations. In any case, a stable blank node identifier defined for one RDF store or serialization is arbitrary, and typically not relatable to the context within which it is used.

This specification defines an algorithm for creating stable blank node identifiers repeatably for different serializations possibly using individualized blank node identifiers of the same RDF graph (dataset) by grounding each blank node through the nodes to which it is connected. As a result, a graph signature can be obtained by hashing a canonical serialization of the resulting canonicalized dataset, allowing for the isomorphism and digital signing use cases. As blank node identifiers can be stable even with other changes to a graph (dataset), in some cases it is possible to compute the difference between two graphs (datasets), for example if changes are made only to ground triples, or if new blank nodes are introduced which do not create an automorphic confusion with other existing blank nodes. If any information which would change the generated blank node identifier, a resulting diff might indicate a greater set of changes than actually exists. Additionally, if the starting dataset is an N-Quads document, it may be possible to correlate the original blank node identifiers used within that N-Quads document with those issued in the canonicalized dataset.

How to Read this Document

This document is a detailed specification for an RDF dataset canonicalization algorithm. The document is primarily intended for the following audiences:

To understand the basics in this specification you must be familiar with basic RDF concepts [[RDF11-CONCEPTS]]. A working knowledge of graph theory and graph isomorphism is also recommended.

Typographical conventions

A conforming processor is a system which can generate the canonical n-quads form of an input dataset consistent with the algorithms defined in this specification.

The algorithms in this specification are normative, because to consistently reproduce the same canonical identifiers, implementations MUST strictly conform to the steps outlined in these algorithms.

Implementers can partially check their level of conformance with this specification by successfully passing the test cases of the RDF Dataset Canonicalization test suite. Note, however, that passing all the tests in the test suite does not imply complete conformance to this specification. It only implies that the implementation conforms to the aspects tested by the test suite.

Terminology

Terms defined by this specification

input dataset
The abstract RDF dataset that is provided as input to the algorithm.
input blank node identifier map
Records any blank node identifiers already assigned to the input dataset. If the input dataset is provided as an N-Quads document, the map relates blank nodes in the abstract input dataset to the blank node identifiers used within the N-Quads document, otherwise, identifiers are assigned arbitrarily for each blank node in the input dataset not previously identified.
Implementations or environments might deal with blank node identifiers more directly; for example, some implementations might retain blank node identifiers in the parsed or abstract dataset. Implementations are expected to reuse these to enable usable mappings between input blank node identifiers and output blank node identifiers outside of the algorithm.
canonicalized dataset
A canonicalized dataset is the combination of the following: A concrete serialization of a canonicalized dataset MUST label all blank nodes using the canonical blank node identifiers.
identifier issuer
An identifier issuer is used to issue new blank node identifiers. It maintains a blank node identifier issuer state.
hash
The lowercase, hexadecimal representation of a message digest.
hash algorithm
The default hash algorithm used by RDFC-1.0, namely, SHA-256 [[FIPS-180-4]].

Implementations MUST support a parameter to define the hash algorithm, MUST support SHA-256 and SHA-384 [[FIPS-180-4]], and SHOULD support the ability to specify other hash algorithms. Using a different hash algorithm will generally result in different output than using the default.

mention
A node is mentioned in a quad if it is a component of that quad, as a subject, predicate, object, or graph name.
mention set
The set of all quads in a dataset that mention a node n is called the mention set of n, denoted Qn.
gossip path
A particular enumeration of every incident mention emanating from a blank node. This recursively includes transitively related mentions until any named node or blank node already labeled by a particular identifier issuer is reached. Gossip paths are encoded and operated on in the RDFC-1.0 algorithm as strings. (See for more information on the construction of gossip paths.)
canonical n-quads form
The canonicalized representation of a quad is defined in . A quad in canonical n-quads form represents a graph name, if present, in the same manner as a subject, and each quad is terminated with a single LF (line feed, code point U+000A).
quad
A tuple composed of subject, predicate, object, and graph name. This is a generalization of an RDF triple along with a graph name.
canonicalization function
A canonicalization function maps RDF datasets into isomorphic datasets [[!RDF11-CONCEPTS]]. Two datasets produce the same canonical result if and only if they are isomorphic. The RDFC-1.0 algorithm implements a canonicalization function. Some datasets may be constructed to prevent this algorithm from terminating in a reasonable amount of time (see ), in which case the algorithm can be considered to be a partial canonicalization function.

Terms defined by cited specifications

string
A string is a sequence of zero or more Unicode characters.
true and false
Values that are used to express one of two possible boolean states.
IRI
An IRI (Internationalized Resource Identifier) is a string that conforms to the syntax defined in [[RFC3987]].
subject
A subject as specified by [[!RDF11-CONCEPTS]].
predicate
A predicate as specified by [[!RDF11-CONCEPTS]].
object
An object as specified by [[!RDF11-CONCEPTS]].
RDF triple
A triple as specified by [[!RDF11-CONCEPTS]].
RDF graph
An RDF graph as specified by [[!RDF11-CONCEPTS]].
graph name
A graph name as specified by [[!RDF11-CONCEPTS]].
default graph
The default graph as specified by [[!RDF11-CONCEPTS]].
RDF dataset
A dataset as specified by [[!RDF11-CONCEPTS]]. For the purposes of this specification, an RDF dataset is considered to be a set of quads
blank node
A blank node as specified by [[!RDF11-CONCEPTS]]. In short, it is a node in a graph that is neither an IRI, nor a literal.
blank node identifier
A blank node identifier as specified by [[!RDF11-CONCEPTS]]. In short, it is a string that begins with _: that is used as an identifier for a blank node. Blank node identifiers are typically implementation-specific local identifiers; this document specifies an algorithm for deterministically specifying them.
Concrete syntaxes, like [[Turtle]] or [[N-Quads]], prepend blank node identifiers with the _: string to differentiate them from other nodes in the graph. This affects the canonicalization algorithm, which is based on calculating a hash over the representations of quads in this format.
Unicode code point order
This refers to determining the order of two Unicode strings (`A` and `B`), using Unicode Codepoint Collation, as defined in [[XPATH-FUNCTIONS]], which defines a total ordering of strings comparing code points. Note that for UTF-8 encoded strings, comparing the byte sequences gives the same result as code point order.

Canonicalization

Canonicalization is the process of transforming an input dataset to its serialized canonical form. That is, any two input datasets that contain the same information, regardless of their arrangement, will be transformed into the same serialized canonical form. The problem requires directed graphs to be deterministically ordered into sets of nodes and edges. This is easy to do when all of the nodes have globally-unique identifiers, but can be difficult to do when some of the nodes do not. Any nodes without globally-unique identifiers must be issued deterministic identifiers.

This specification defines a canonicalized dataset to include stable identifiers for blank nodes, practical uses of which will always generate a canonical serialization of such a dataset.

In time, there may be more than one canonicalization algorithm and, therefore, for identification purposes, this algorithm is named the "RDF Canonicalization algorithm version 1.0" (RDFC-1.0).

provides an overview of RDFC-1.0, with steps 1 through 7 corresponding to the various steps described in .

The image represents an overview of the RDFC-1.0 algorithm. The Input Document is deserialized into the Input Dataset and Input Blank Node Identifier Map. Canonicalization steps 1-6 are executed resulting in the Canonicalized Dataset including the Input Blank Node Identifier Map and Issued Identifiers Map. Step 7 of the Canonicalization algorithm creates the canonical n-quads form of the Canonicalized Dataset.

An illustrated overview of the RDFC-1.0 algorithm.
Image available in SVG .

Overview

To determine a canonical labeling, RDFC-1.0 considers the information connected to each blank node. Nodes with unique first degree information can immediately be issued a canonical identifier via the Issue Identifier algorithm. When a node has non-unique first degree information, it is necessary to determine all information that is transitively connected to it throughout the entire dataset. defines a node’s first degree information via its first degree hash.

Hashes are computed from the information of each blank node. These hashes encode the mentions incident to each blank node. The hash of a string s, is the lower-case, hexadecimal representation of the result of passing s through a cryptographic hash function. By default, RDFC-1.0 uses the SHA-256 hash algorithm [[FIPS-180-4]].

The "degree" terminology is used within this specification as colloquial way of describing the eccentricity or radius of any two nodes within a dataset. This concept is also related to "degrees of separation", as in, for example, "six degrees of separation". Nodes with unique first degree information can be considered nodes with a radius of one.

Canonicalization State

When performing the steps required by the canonicalization algorithm, it is helpful to track state in a data structure called the canonicalization state. The information contained in the canonicalization state is described below.

blank node to quads map
A map that relates a blank node identifier to the quads in which they appear in the input dataset.
hash to blank nodes map
A map that relates a hash to a list of blank node identifiers.
canonical issuer
An identifier issuer, initialized with the prefix c14n (short for canonicalization), for issuing canonical blank node identifiers.
Mapping all blank nodes to use this identifier spec means that an RDF dataset composed of two different RDF graphs will issue different identifiers than that for the graphs taken independently. This may happen anyway, due to automorphisms, or overlapping statements, but an identifier based on the resulting hash along with an issue sequence number specific to that hash would stand a better chance of surviving such minor changes, and allow the resulting information to be useful for RDF Diff.

Blank Node Identifier Issuer State

The canonicalization algorithm issues identifiers to blank nodes. The Issue Identifier algorithm uses an identifier issuer to accomplish this task. The information an identifier issuer needs to keep track of is described below.

identifier prefix
The identifier prefix is a string that is used at the beginning of an blank node identifier. It should be initialized to a string that is specified by the canonicalization algorithm. When generating a new blank node identifier, the prefix is concatenated with a identifier counter. For example, c14n is a proper initial value for the identifier prefix that would produce blank node identifiers like c14n1.
identifier counter
A counter that is appended to the identifier prefix to create an blank node identifier. It is initialized to 0.
issued identifiers map
An ordered map that relates blank node identifiers to issued identifiers, to prevent issuance of more than one new identifier per existing identifier, and to allow blank nodes to be assigned identifiers some time after issuance.

Canonicalization Algorithm

The canonicalization algorithm converts an input dataset into a canonicalized dataset. This algorithm will assign deterministic identifiers to any blank nodes in the input dataset.

Overview

RDFC-1.0 canonically labels an RDF dataset by assigning each blank node a canonical identifier. In RDFC-1.0, an RDF dataset D is represented as a set of quads of the form `< s, p, o, g >` where the graph component `g` is empty if and only if the triple `< s, p, o >` is in the default graph. It is expected that, for two RDF datasets, RDFC-1.0 returns the same canonically labeled list of quads if and only if the two datasets are isomorphic (i.e., the same modulo blank node identifiers).

RDFC-1.0 consists of several sub-algorithms. These sub-algorithms are introduced in the following sub-sections. First, we give a high level summary of RDFC-1.0.

  1. Initialization. Initialize the state needed for the rest of the algorithm using . Also initialize the canonicalized dataset using the input dataset (which remains immutable) the input blank node identifier map (retaining blank node identifiers from the input if possible, otherwise assigning them arbitrarily); the issued identifiers map from the canonical issuer is added upon completion of the algorithm.
  2. Compute first degree hashes. Compute the first degree hash for each blank node in the dataset using .
  3. Canonically label unique nodes. Assign canonical identifiers via , in Unicode code point order, to each blank node whose first degree hash is unique.
  4. Compute N-degree hashes for non-unique nodes. For each repeated first degree hash (proceeding in Unicode code point order), compute the N-degree hash via of every unlabeled blank node that corresponds to the given repeated hash.
  5. Canonically label remaining nodes. In Unicode code point order of the N-degree hashes, issue canonical identifiers to each corresponding blank node using . If more than one node produces the same N-degree hash, the order in which these nodes receive a canonical identifier does not matter.
  6. Finish. Return the serialized canonical form of the canonicalized dataset. Alternatively, return the canonicalized dataset containing the input blank node identifier map and issued identifiers map.

Examples

Algorithm

The following algorithm will run with a minimal number of iterations in each step for typical input datasets. In some extreme cases, the algorithm can behave poorly, particularly in Step 5. Implementations MUST prevent against potential denial-of-service attacks. See for further information.

Implementations can consider placing limits on the number of calls to based on the number of blank nodes in the hash to blank nodes map. For most typical datasets, more than a couple of iterations on per blank node would be unusual.

  1. Create the canonicalization state. If the input dataset is an N-Quads document, parse that document into a dataset in the canonicalized dataset, retaining any blank node identifiers used within that document in the input blank node identifier map; otherwise arbitrary identifiers are assigned for each blank node.
    Explanation

    This has the effect of initializing the blank node to quads map, and the hash to blank nodes map, as well as instantiating a new canonical issuer.

    After this algorithm completes, the input blank node identifier map state and canonical issuer may be used to correlate blank nodes used in the input dataset with both their original identifiers, and associated canonical identifiers.

  2. For every quad Q in input dataset:
    1. For each blank node that is a component of Q, add a reference to Q from the [= map/entry | map entry =] for the blank node identifier identifier in the blank node to quads map, creating a new entry if necessary, using the identifier for the blank node found in the input blank node identifier map.
      Explanation

      This establishes the blank node to quads map, relating each blank node with the set of quads of which it is a component, via the map for each blank node in the input dataset to its assigned identifier.

      Literal components of quads are not subject to any normalization. As noted in Section 3.3 of [[RDF11-CONCEPTS]], literal term equality is based on the lexical form, rather than the literal value, so two literals `"01"^^xsd:integer` and `"1"^^xsd:integer` are treated as distinct resources.

    Logging

    Log the state of the blank node to quads map:

                  
                
  3. For each [= map/key =] n in the blank node to quads map:
    Explanation

    This step creates a hash for every blank node in the input document. Some blank nodes will lead to a unique hash, while other blank nodes may share a common hash.

    1. Create a hash, hf(n), for n according to the Hash First Degree Quads algorithm.
    2. Append n to the value associated to hf(n) in hash to blank nodes map, creating a new entry if necessary.
    Logging

    Log the results from the Hash First Degree Quads algorithm.

                  
                
  4. For each hash to identifier list [= map/entry | map entry =] in hash to blank nodes map, code point ordered by hash:
    Explanation

    This step establishes the canonical identifier for blank nodes having a unique hash, which are recorded in the canonical issuer.

    1. If identifier list has more than one entry, continue to the next mapping.
    2. Use the Issue Identifier algorithm, passing canonical issuer and the single blank node identifier, identifier in identifier list to issue a canonical replacement identifier for identifier.
    3. Remove the [= map/entry | map entry =] for hash from the hash to blank nodes map.
    Logging

    Log the assigned canonical identifiers.

                  
                
  5. For each hash to identifier list [= map/entry | map entry =] in hash to blank nodes map, code point ordered by hash:
    Explanation

    This step establishes the canonical identifier for blank nodes having a shared hash. This is done by creating unique blank node identifiers for all blank nodes traversed by the Hash N-Degree Quads algorithm, running through each blank node without a canonical identifier in the order of the hashes established in the previous step.

    Logging

    Log hash and identifier list for this iteration.

                  
                
    1. Create hash path list where each item will be a result of running the Hash N-Degree Quads algorithm.
      Explanation

      This list will be populated in step 5.2, and will establish an order for those blank nodes sharing a common first-degree hash.

    2. For each blank node identifier n in identifier list:
      1. If a canonical identifier has already been issued for n, continue to the next blank node identifier.
      2. Create temporary issuer, an identifier issuer initialized with the prefix b.
      3. Use the Issue Identifier algorithm, passing temporary issuer and n, to issue a new temporary blank node identifier bn to n.
      4. Run the Hash N-Degree Quads algorithm, passing the canonicalization state, n for identifier, and temporary issuer, appending the result to the hash path list.
        Logging

        Include logs for each call to Hash N-Degree Quads algorithm.

                              
                            
    3. For each result in the hash path list, code point ordered by the hash in result:
      Explanation

      The previous step created temporary identifiers for the blank nodes sharing a common first degree hash, which is now used to generate their canonical identifiers.

      1. For each blank node identifier, existing identifier, that was issued a temporary identifier by identifier issuer in result, issue a canonical identifier, in the same order, using the Issue Identifier algorithm, passing canonical issuer and existing identifier.
        Explanation

        In Step 5.2, hash path list was created with an ordered set of results. Each result contained a temporary issuer which recorded temporary identifiers associated with a particular blank node identifier in identifier list. This step processes each returned temporary issuer, in order, and allocates canonical identifiers to the temporary identifier mappings contained within each temporary issuer, creating a full order on the remaining blank nodes with unissued canonical identifiers.

      Logging

      Log newly issued canonical identifiers.

                        
                      
  6. Add the issued identifiers map from the canonical issuer to the canonicalized dataset.
    Explanation

    This step adds the issued identifiers map from the canonical issuer to the canonicalized dataset, the [= map/key | keys =] in the issued identifiers map are [= map/entry | map entries =] in the input blank node identifier map.

    Logging

    Log the state of the canonical issuer at the completion of the algorithm.

                  
                
  7. Return the serialized canonical form of the canonicalized dataset. Upon request, alternatively (or additionally) return the canonicalized dataset itself, which includes the input blank node identifier map, and issued identifiers map from the canonical issuer.

    Technically speaking, one implementation might return a canonicalized dataset that maps particular blank nodes to different identifiers than another implementation, however, this only occurs when there are isomorphisms in the dataset such that a canonically serialized expression of the dataset would appear the same from either implementation.

    Explanation

    The serialized canonical form is an N-Quads document where the blank node identifiers are taken from the canonical identifiers associated with each blank node.

    The canonicalized dataset is composed of the original input dataset, the input blank node identifier map, containing identifiers for each blank node in the input dataset, and the canonical issuer, containing an issued identifiers map mapping the identifiers in the input blank node identifier map to their canonical identifiers.

Issue Identifier Algorithm

This algorithm issues a new blank node identifier for a given existing blank node identifier. It also updates state information that tracks the order in which new blank node identifiers were issued. The order of issuance is important for canonically labeling blank nodes that are isomorphic to others in the dataset.

Overview

The algorithm maintains an issued identifiers map to relate an existing blank node identifier from the input dataset to a new blank node identifier using a given identifier prefix (c14n) with new identifiers issued by appending an incrementing number. For example, when called for a blank node identifier such as e3, it might result in a issued identifier of c14n1.

Algorithm

The algorithm takes an identifier issuer I and an existing identifier as inputs. The output is a new issued identifier. The steps of the algorithm are:

  1. If there is a [= map/entry | map entry =] for existing identifier in issued identifiers map of I, return it.
  2. Generate issued identifier by concatenating identifier prefix with the string value of identifier counter.
  3. Add an [= map/entry =] mapping existing identifier to issued identifier to the issued identifiers map of I.
  4. Increment identifier counter.
  5. Return issued identifier.

Hash First Degree Quads

This algorithm calculates a hash for a given blank node across the quads in a dataset in which that blank node is a component. If the hash uniquely identifies that blank node, no further examination is necessary. Otherwise, a hash will be created for the blank node using the algorithm in invoked via .

Overview

To determine whether the first degree information of a node n is unique, a hash is assigned to its mention set, Qn. The first degree hash of a blank node n, denoted hf(n), is the hash that results from when passing n. Nodes with unique first degree hashes have unique first degree information.

For consistency, blank node identifiers used in Qn are replaced with placeholders in a canonical n-quads serialization of that quad. Every blank node component is replaced with either a or z, depending on if that component is n or not.

The resulting serialized quads are then code point ordered, concatenated, and hashed. This hash is the first degree hash of n, hf(n).

Examples

Algorithm

This algorithm takes the canonicalization state and a reference blank node identifier as inputs.

  1. Initialize nquads to an empty list. It will be used to store quads in canonical n-quads form.
  2. Get the list of quads quads from the [= map/entry | map entry =] for reference blank node identifier in the blank node to quads map.
  3. For each quad quad in quads:
    1. Serialize the quad in canonical n-quads form with the following special rule:
      1. If any component in quad is an blank node, then serialize it using a special identifier as follows:
        1. If the blank node's existing blank node identifier matches the reference blank node identifier then use the blank node identifier a, otherwise, use the blank node identifier z.
  4. Sort nquads in Unicode code point order.
  5. Return the hash that results from passing the sorted and concatenated nquads through the hash algorithm.
    Logging

    Log the inputs and result of running this algorithm.

                  
                

Hash N-Degree Quads

This algorithm calculates a hash for a given blank node across the quads in a dataset in which that blank node is a component for which the hash does not uniquely identify that blank node. This is done by expanding the search from quads directly referencing that blank node (the mention set), to those quads which contain nodes which are also components of quads in the mention set, called the gossip path. This process proceeds in every greater degrees of indirection until a unique hash is obtained.

Overview

Usually, when trying to determine if two nodes in a graph are equivalent, you simply compare their identifiers. However, what if the nodes don't have identifiers? Then you must determine if the two nodes have equivalent connections to equivalent nodes all throughout the whole graph. This is called the graph isomorphism problem. This algorithm approaches this problem by considering how one might draw a graph on paper. You can test to see if two nodes are equivalent by drawing the graph twice. The first time you draw the graph the first node is drawn in the center of the page. If you can draw the graph a second time such that it looks just like the first, except the second node is in the center of the page, then the nodes are equivalent. This algorithm essentially defines a deterministic way to draw a graph where, if you begin with a particular node, the graph will always be drawn the same way. If two graphs are drawn the same way with two different nodes, then the nodes are equivalent. A hash is used to indicate a particular way that the graph has been drawn and can be used to compare nodes.

When two blank nodes have the same first degree hash, extra steps must be taken to detect global, or N-degree, distinctions. All information that is in any way connected to the blank node n through other blank nodes, even transitively, must be considered.

To consider all transitive information, the algorithm traverses and encodes all possible paths of incident mentions emanating from n, called gossip paths, that reach every unlabeled blank node connected to n. Each unlabeled blank node is assigned a temporary identifier in the order in which it is reached in the gossip path being explored. The mentions that are traversed to reach connected blank nodes are encoded in these paths via related hashes. This provides a deterministic way to order all paths coming from n that reach all blank nodes connected to n without relying on input blank node identifiers.

This algorithm works in concert with the main canonicalization algorithm to produce a unique, deterministic identifier for a particular blank node. This hash incorporates all of the information that is connected to the blank node as well as how it is connected. It does this by creating deterministic paths that emanate out from the blank node through any other adjacent blank nodes.

Ultimately, the algorithm selects the shortest gossip path (based on its encoding as a string), distributing canonical identifiers to the unlabeled blank nodes in the order in which they appear in this path. The hash of this encoded shortest path, called the N-degree hash of n, distinguishes n from other blank nodes in the dataset.

For clarity, we consider a gossip path encoded via the string s to be shortest provided that:

  1. The length of s is less than or equal to the length of any other gossip path string s′.
  2. If s and s′ have the same length (as strings), then s is code point ordered less than or equal to s′.

For example, abc is shorter than bbc, whereas abcd is longer than bcd.

The following provides a high level outline for how the N-degree hash of n is computed along the shortest gossip path. Note that the full algorithm considers all gossip paths, ultimately returning the hash of the shortest encoded path.

  1. Compute related hashes. Compute the related hash Hn set for n, i.e., all first degree mentions between n and another blank node. Note that this includes both unlabeled blank nodes and those already issued a canonical identifier (labeled blank nodes).
  2. Explore mentions. Given the related hash x in Hn, record x in the data to hash Dn. Determine whether each blank node reachable via the mention with related hash x has already received an identifier.
    1. Record the identifiers of labeled nodes. If a blank node already has an identifier, record its identifier in Dn once for every mention with related hash x. Skip to the next related hash in Hn and repeat step 2.
    2. Distribute and record temporary identifiers to unlabeled nodes. For each unlabeled blank node, assign it a temporary identifier according to the order in which it is reached in the gossip path, recording its given identifier in Dn (including repetitions). Add each unlabeled node to the recursion list Rn(x) in this same order (omitting repetitions).
    3. Recurse on newly labeled nodes. For each ni in Rn(x)
      1. Record its identifier in Dn
      2. Append < r(i) > to Dn where r(i) is the data to hash that results from returning to step 1, replacing n with ni.
  3. Compute the N-degree hash of n. Hash Dn to return the N-degree hash of n, namely hN(n). Return the updated issuer In that has now distributed temporary identifiers to all unlabeled blank nodes connected to n.

As described above in step 2.3, HN recurses on each unlabeled blank node when it is first reached along the gossip path being explored. This recursion can be visualized as moving along the path from n to the blank node ni that is receiving a temporary identifier. If, when recursing on ni, another unlabeled blank node nj is discovered, the algorithm again recurses. Such a recursion traces out the gossip path from n to nj via ni.

The recursive hash r(i) is the hash returned from the completed recursion on the node ni when computing hN(n). Just as hN(n) is the hash of Dn, we denote the data to hash in the recursion on ni as Di. So, r(i) = h(Di). For each related hash xHn, Rn(x) is called the recursion list on which the algorithm recurses.

Examples

Algorithm

The inputs to this algorithm are the canonicalization state, the identifier for the blank node to recursively hash quads for, and path identifier issuer which is an identifier issuer that issues temporary blank node identifiers. The output from this algorithm will be a hash and the identifier issuer used to help generate it.

Logging

Log the inputs to the algorithm.

          
        
  1. Create a new map Hn for relating hashes to related blank nodes.
  2. Get a reference, quads, to the list of quads from the [= map/entry | map entry =] for identifier in the blank node to quads map.
    Explanation

    quads is the mention set of identifier.

    Logging

    Log the quads from the mention set of identifier.

                  
                
  3. For each quad in quads:
    Explanation

    This loop calculates the related hash Hn for other blank nodes within the mention set of identifier.

    1. For each component in quad, where component is the subject, object, or graph name, and it is a blank node that is not identified by identifier:
      1. Set hash to the result of the Hash Related Blank Node algorithm, passing the blank node identifier for component as related, quad, issuer, and position as either s, o, or g based on whether component is a subject, object, graph name, respectively.
      2. Add a mapping of hash to the blank node identifier for component to Hn, adding an entry as necessary.
    Logging

    Include the logs for each iteration of the Hash Related Blank Node algorithm and the resulting Hn.

                  
                
  4. Create an empty string, data to hash.
  5. For each related hash to blank node list mapping in Hn, code point ordered by related hash:
    Explanation

    This loop explores the gossip paths for each related blank node sharing a common hash to identifier finding the shortest such path (chosen path). This determines how canonical identifiers for otherwise commonly hashed blank nodes are chosen.

    Each path is represented by the concatenation of the identifiers for each related blank node – either the issued identifier, or a temporary identifier created using a copy of issuer. Those for which temporary identifiers were issued are later recursed over using this algorithm.

    Logging

    Log the value of related hash and state of data to hash.

                  
                
    1. Append the related hash to the data to hash.
    2. Create a string chosen path.
    3. Create an unset chosen issuer variable.
    4. For each permutation p of blank node list:
      Logging

      Log each permutation p.

                        
                      
      1. Create a copy of issuer, issuer copy.
      2. Create a string path.
      3. Create a recursion list, to store blank node identifiers that must be recursively processed by this algorithm.
      4. For each related in p:
        1. If a canonical identifier has been issued for related by canonical issuer, append the string _:, followed by the canonical identifier for related, to path.
          Explanation

          A canonical identifier may have been generated before calling this algorithm, if it was issued from an earlier call to Hash First Degree Quads algorithm. There is no reason to recurse and apply the algorithm to any related blank node that has already been assigned a canonical identifier. Furthermore, using the canonical identifier also further distinguishes it from any temporary identifier, allowing for even greater efficiency in finding the chosen path.

        2. Otherwise:
          1. If issuer copy has not issued an identifier for related, append related to recursion list.
            Explanation

            Temporarily labeled nodes have identifiers recorded in issuer copy, which is later used to recursively call this algorithm, so that eventually all nodes are given canonical identifiers.

          2. Use the Issue Identifier algorithm, passing issuer copy and the related, and append the string _:, followed by the result, to path.
        3. If chosen path is not empty and the length of path is greater than or equal to the length of chosen path and path is greater than chosen path when considering code point order, then skip to the next permutation p.
          Explanation

          If path is already longer than the prospective chosen path, we can terminate this iteration early.

        Explanation

        path is used to generate a hash at a later step; in this respect, it is similar to the Hash First Degree Quads algorithm which uses the serialization of quads in nquads for hashing. For the sake of consistency, the nquad representation of blank node identifiers is used in these steps, hence the usage of the _: string.

        Logging

        Log related and path.

                              
                            
      5. For each related in recursion list:
        Explanation

        The prospective path is extended with the hash resulting from recursively calling this algorithm on each related blank node issued a temporary identifier.

        Logging

        Log recursion list and path.

                              
                            
        1. Set result to the result of recursively executing the Hash N-Degree Quads algorithm, passing the canonicalization state, related for identifier, and issuer copy for path identifier issuer.
          Logging

          Log related and include logs for each recursive call to Hash N-Degree Quads algorithm.

                                    
                                  
        2. Use the Issue Identifier algorithm, passing issuer copy and related; append the string _:, followed by the result, to path.
        3. Append <, the hash in result, and > to path.
        4. Set issuer copy to the identifier issuer in result.
        5. If chosen path is not empty and the length of path is greater than or equal to the length of chosen path and path is greater than chosen path when considering code point order, then skip to the next p.
          Explanation

          If path is already longer than the prospective chosen path, we can terminate this iteration early.

      6. If chosen path is empty or path is less than chosen path when considering code point order, set chosen path to path and chosen issuer to issuer copy.
    5. Append chosen path to data to hash.
      Logging

      Log chosen path and data to hash.

                        
                      
    6. Replace issuer, by reference, withchosen issuer.
  6. Return issuer and the hash that results from passing data to hash through the hash algorithm.
    Logging

    Log issuer and results from passing data to hash through the hash algorithm.

                  
                

Serialization

This section describes the process of creating a serialized [[N-Quads]] representation of a canonicalized dataset.

The serialized canonical form of a canonicalized dataset is an N-Quads document [[N-QUADS]] created by representing each quad from the canonicalized dataset in canonical n-quads form, sorting them into code point order, and concatenating them. (Note that each canonical N-Quads statement ends with a new line, so no additional separators are needed in the concatenation.) The resulting document has a media type of `application/n-quads`, as described in C. N-Quads Internet Media Type, File Extension and Macintosh File Type of [[N-QUADS]].

When serializing quads in canonical n-quads form, components which are blank nodes MUST be serialized using the canonical label associated with each blank node from the issued identifiers map component of the canonicalized dataset.

Privacy Considerations

The nature of the canonicalization algorithm inherently correlates its output, i.e., the canonical labels and the sorted order of quads, with the input dataset. This could pose issues, particularly when dealing with datasets containing personal information. For example, even if certain information is removed from the canonicalized dataset for some privacy-respecting reason, there remains the possibility that a third party could infer the omitted data by analyzing the canonicalized dataset. If it is necessary to decouple the canonicalization algorithm's input and output, some suitable post-processing methods for the output of the canonicalization should be performed. This specification has been designed to help make additional processing easier, but other specifications that build on top of this one are responsible for providing any specific details. See Selective Disclosure in [[[VC-DATA-INTEGRITY]]] [[VC-DATA-INTEGRITY]] for more details about such post-processing methods.

Security Considerations

Dataset Poisoning

The canonicalization algorithm examines every difference in the information connected to blank nodes in order to ensure that each will properly receive its own canonical identifier. This process can be exploited by attackers to construct datasets which are known to take large amounts of computing time to canonicalize, but that do not express useful information or express it using unnecessary complexity. Implementers of the algorithm are expected to add mitigations that will, by default, abort canonicalizing problematic inputs.

Suggested mitigations include, but are not limited to:

Additionally, software that uses implementations of the algorithm can employ best-practice schema validation to reject data that does not meet application requirements, thereby preventing useless poison datasets from being processed. However, such mitigations are application specific and not directly applicable to implementers of the canonicalization algorithm itself.

Insecure Hash Algorithms

It is possible that the default hash algorithm used by RDFC-1.0 might become insecure at some point in the future. To mitigate this, this algorithm and implementations of it can be parameterized to use a different hash function, without the need to make any changes to the canonicalization algorithm itself. However, using a different hash algorithm will generally lead to different results.

Use Cases

Examples

Duplicate Paths

This example illustrates a more complicated example where the same paths through blank nodes are duplicated in a graph, but use different blank node identifiers.

The image represents the graph described in the following code block .

An illustration of a graph with duplicated paths.
Image available in SVG .
      
    

The following is a summary of the more detailed execution log found here.

Double Circle

This example illustrates another complicated example of nodes that are doubly connected in opposite directions.

The image represents the graph described in the following code block .

An illustration of a graph back and forth links to nodes.
Image available in SVG .
      
    

The example is not explored in detail, but the execution log found here shows examples of more complicated pathways through the algorithm

Dataset with Blank Node Named Graph

This example illustrates an example of a dataset, where one graph is named using a blank node, which is also the object of a triple in the default graph.

The image represents the dataset described in the following code block .

An illustration of a dataset containing a graph named with a blank node.
Image available in SVG .
      
    

The following is a summary of the more detailed execution log found here.

A Canonical form of N-Quads

This section defines a canonical form of N-Quads which has a completely specified layout. The grammar for the language remains unchanged.

Canonical N-Quads updates and extends Canonical N-Triples in [[N-TRIPLES]] to include graphLabel.

While the N-Quads syntax [[N-QUADS]] allows choices for the representation and layout of RDF data, the canonical form of N-Quads provides a unique syntactic representation of any quad. Each code point can be represented by only one of UCHAR, ECHAR, or unencoded character, where the relevant production allows for a choice in representation. Each quad is represented entirely on a single line with specified white space.

Canonical N-Quads has the following additional constraints on layout:

URDNA2015

[[[CCG-RDC-FINAL]]] [[CCG-RDC-FINAL]] describes "Universal RDF Dataset Normalization Algorithm 2015" (URDNA2015), essentially the same algorithm as RDFC-1.0, and generally implementations implementing URDNA2015 should be compatible with this specification. The minor change is in the canonical n-quads form where some control characters were previously represented without escaping. The version of the algorithm defined in clarifies the representation of simple literals and the characters within STRING_LITERAL_QUOTE that are encoded using ECHAR.

URGNA2012

A previous version of this algorithm has light deployment. For purposes of identification, the algorithm is called the "Universal RDF Graph Canonicalization Algorithm 2012" (URGNA2012), and differs from the stated algorithm in the following ways:

Changes since the First Public Working Draft of 24 November 2022

Acknowledgements

The editors would like to thank Jeremy Carroll for his work on the graph canonicalization problem, Andy Seaborne and Gavin Carothers for providing valuable feedback and testing input for the algorithm defined in this specification, Sir Tim Berners-Lee for his thoughts on graph canonicalization over the years, Jesús Arias Fisteus for his work on a similar algorithm, and Aiden Hogan, whose publication [[Hogan-Canonical-RDF]] provided an important contemporary analysis of the canonicalization problem and served as an independent justification of the development of RDFC-1.0.

This specification is based on work done in the W3C Credentials Community Group published as [[CCG-RDC-FINAL]]. Contributors to the Community Group Final Report include: Blake Regalia, Dave Longley, David Lehn, David Lozano Jarque, Gregg Kellogg, Manu Sporny, Markus Sabadello, Matt Collier, and Sebastian Schmittner.

Portions of the work on this specification have been funded by the European Union's StandICT.eu 2023 program under sub-grantee contract numbers No. 08/12 and 09/25. The content of this specification does not necessarily reflect the position or the policy of the European Union and no official endorsement should be inferred.

Portions of the work on this specification have also been funded by the U.S. Department of Homeland Security's Silicon Valley Innovation Program under contracts 70RSAT21T00000020 and 70RSAT23T00000006. The content of this specification does not necessarily reflect the position or the policy of the U.S. Government and no official endorsement should be inferred.