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The Network Data Structure in Computing

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Marko Rodriguez
Marko Rodriguez

The document discusses network data structures and semantic networks. It provides examples of undirected, directed, and semantic networks. It describes how PageRank can be applied to semantic networks using grammar-based random walkers that follow the relationships between nodes defined in an ontology. It also lists related publications by the author on modeling systems and computations as semantic networks.

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The Network Data Structure in Computing Marko A. Rodriguez Los Alamos National Laboratory Vrije Universiteit Brussel [email_address] http://cnls.lanl.gov/~marko
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About me. Marko Antonio Rodriguez. Bachelors of Science in Cognitive Science from U.C. San Diego. Minor in the Arts in Computer Music from U.C. San Diego. Masters of Science in Computer Science from U.C. Santa Cruz. Visiting Researcher at the Center for Evolution, Complexity, and Cognition at the Free University of Brussels. Ph.D. in Computer Science from U.C. Santa Cruz. Researcher at the Los Alamos National Laboratory since 2005.
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Research trends. MESUR : Metrics from Scholarly Usage of Resources. ( http://www.mesur.org ) Neno / Fhat : A Semantic Network Programming Language and Virtual Machine Architecture. ( http://neno.lanl.gov ) C D M S : Collective Decision Making Systems. ( http://cdms.lanl.gov )
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What is a network? A network is a data structure that is used to connect vertices /nodes/dots by means of edges /links/lines. Networks are everywhere. Social : friendship, trust, communication, collaboration. Technological : web-pages, communication, software dependencies, circuits. Scholarly : journals, authors, articles, institutions. Natural : protein interaction, neural, food web.
5
The undirected network. There is the undirected network of common knowledge. Sometimes called an undirected single-relational network. e.g. vertex i and vertex j are “related”. The semantic of the edge denotes the network type . e.g. friendship network, collaboration network, etc. i j
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Example undirected network. Herbert Marko Aric Ed Zhiwu Alberto Jen Johan Luda Stephan Whenzong
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The directed network. Then there is the directed network of common knowledge. Sometimes called a directed single-relational network. For example, vertex i is related to vertex j , but j is not related to i . i j
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Example directed network. Muskrat Bear Fish Fox Meerkat Lion Human Wolf Deer Beetle Hyena
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The semantic network. Finally, there is the semantic network Sometimes called a directed multi-relational network. For example, vertex i is related to vertex j by the semantic s , but j is not related to i by the semantic s . i j s
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Example semantic network. SantaFe Marko NewMexico Ryan California UnitedStates LANL livesIn worksWith cityOf originallyFrom stateOf stateOf locatedIn hasLab Cells Atoms madeOf madeOf researches Oregon southOf hasResident Arnold governerOf northOf
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Google’s PageRank. PageRank Used to rank web-pages that are connected by citation (hyper-link). Note: this image was stolen off the web from somewhere.
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The components to calculate a stationary probability distribution. Take a single “random walker”. Place that random walker on any random vertex in the network. At every time step, the random walker transitions from its current node to an adjacent node in the network (i.e. takes a random outgoing edge from its current node.) Anytime the random walker is at a node, increment a “times visited” counter by 1. Let this algorithm run for an “infinite” amount of time. Normalize the “times visited” counters. That is your centrality vector. a 1 0.0123
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Random walker example. a c b d 0 0 0 0
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Random walker example. a c b d 1 0 0 0
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Random walker example. a c b d 1 0 1 0
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Random walker example. a c b d 1 0 1 1
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Random walker example. a c b d 1 1 1 1
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Random walker example. a c b d 1 1 2 1
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Random walker example. a c b d 1 2 2 1
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Random walker example. a c b d 2 2 2 1
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Random walker example. a c b d 2 2 3 1
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Random walker example. a c b d 2 2 3 2
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Random walker example. a c b d 2 3 3 2
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Random walker example. a c b d 2 3 4 2
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Random walker example. a c b d 66785 133310 133321 66784
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Random walker example. a c b d 0.167 0.332 0.332 0.167
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Breather.
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Example semantic network. SantaFe Marko NewMexico Ryan California UnitedStates LANL livesIn worksWith cityOf originallyFrom stateOf stateOf locatedIn hasLab Cells Atoms madeOf madeOf researches Oregon southOf hasResident Arnold governerOf northOf
29
What is the Semantic Web? The figurehead of the Semantic Web initiative, Tim Berners-Lee, describes the Semantic Web as “ ... an extension of the current web in which information is given well-defined meaning, better enabling computers and people to work in cooperation. ” Perhaps not the best definition. It implies a particular application space--namely the “web metadata and intelligent agents” space. My definition is that the Semantic Web is “ a distributed, standardized semantic network data model--a URG (Uniform Resource Graph). It’s a uniform way of graphing resources. ”
30
What is a resource? Resource = Anything. Anything that can be identified. The Uniform Resource Identifier (URI): <scheme name> : <hierarchical part> [ ? <query> ] [ # <fragment> ] http://www.lanl.gov urn:uuid:550e8400-e29b-41d4-a716-446655440000 urn:issn:0892-3310 http://www.lanl.gov#MarkoRodriguez prefix it to make it easier on the eyes -- lanl:MarkoRodriguez The Semantic Web “ first identify it, then relate it! ”
31
The technologies of the Semantic Web. Resource Description Framework (RDF): The foundation technology of the Semantic Web. RDF is a highly-distributed, semantic network data model. In RDF, URIs and literals (e.g. ints, doubles, strings) are related to one another in triples. <lanl:marko> <lanl:worksWith> <lanl:jhw> <lanl:jhw> <lanl:wrote> <lanl:LAUR-07-2028> <lanl:LAUR-07-2028> <lanl:hasTitle> “Web-Based Collective Decision Making Systems”^^<xsd:string> RDF Schema (RDFS): The ontology is to the Semantic Web as the schema is to the relational database. “ Anything of rdf:type lanl:Human can lanl:drive anything of rdf:type lanl:Car .”
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RDF and RDFS. lanl:marko lanl:cookie lanl:Human lanl:Food lanl:isEating rdf:type rdf:type lanl:isEating rdfs:domain rdfs:range ontology instance RDF is not a syntax. It’s a data model. Various syntaxes exist to encode RDF including RDF/XML, N-TRIPLE, TRiX, N3, etc.
33
PageRank in a semantic network? lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote ? lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type ? ?
34
Components of a grammar-based walker. A walker . Discrete element. A grammar . An abstract representation of legal path for the walker take. e.g. “you can traverse a lanl:friendOf edge from a lanl:Human to another lanl:Human .” Also includes rules: “increment a counter.”, “don’t ever return to this vertex.” A data set that respects the ontological “expectations” of the grammar.
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Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 0 0 0 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
36
Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.” 1 0 0
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Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 1 0 0 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
38
Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 1 0 1 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
39
Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 1 0 1 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
40
Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 2 0 1 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
41
Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 2 0 1 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
42
Grammars create implicit relationships. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type lanl:hasCoauthor
43
Conclusions. Many systems can be represented as a network. The semantic network is a more expressive, though less studied data model. The grammar technique can be used to port many of the common network analysis algorithms to the semantic network domain.
44
Related publications. Rodriguez, M.A., Watkins, J.H., Bollen, J., Gershenson, C., “ Using RDF to Model the Structure and Process of Systems ”, International Conference on Complex Systems, Boston, Massachusetts, LAUR-07-5720, October 2007. Rodriguez, M.A., Bollen, J., Van de Sompel, H., “ A Practical Ontology for the Large-Scale Modeling of Scholarly Artifacts and their Usage ”, 2007 ACM/IEEE Joint Conference on Digital Libraries, pages 278-287, Vancouver, Canada, ACM/IEEE Computing, doi:10.1145/1255175.1255229, LA-UR-07-0665, June 2007. Rodriguez, M.A., &quot;Social Decision Making with Multi-Relational Networks and Grammar-Based Particle Swarms &quot;, 2007 Hawaii International Conference on Systems Science (HICSS), pages 39-49, Waikoloa, Hawaii, IEEE Computer Society, ISSN: 1530-1605, doi:10.1109/HICSS.2007.487, LA-UR-06-2139, January 2007. Rodriguez, M.A., &quot; A Multi-Relational Network to Support the Scholarly Communication Process &quot;, International Journal of Public Information Systems, volume 2007, issue 1, pages 13-29, ISSN: 1653-4360, LA-UR-06-2416, March 2007. Rodriguez, M.A., “ Mapping Semantic Networks to Undirected Networks ”, LA-UR-07-5287, August 2007. Rodriguez, M.A., Watkins, J.H., “ Grammar-Based Geodesics in Semantic Networks ”, LA-UR-07-4042, June 2007. Rodriguez, M.A., Bollen, J., “ Modeling Computations in a Semantic Network ”, LA-UR-07-3678, May 2007. Rodriguez, M.A., “ General-Purpose Computing on a Semantic Network Substrate ”, LA-UR-07-2885, April 2007. Rodriguez, M.A., “ Grammar-Based Random Walkers in Semantic Networks ”, Knowledge-Based Systems, Elsevier, LA-UR-06-7791, in press, 2007.
The Network Data Structure in Computing Marko A. Rodriguez Los Alamos National Laboratory Vrije Universiteit Brussel [email_address] http://cnls.lanl.gov/~marko
About me. Marko Antonio Rodriguez. Bachelors of Science in Cognitive Science from U.C. San Diego. Minor in the Arts in Computer Music from U.C. San Diego. Masters of Science in Computer Science from U.C. Santa Cruz. Visiting Researcher at the Center for Evolution, Complexity, and Cognition at the Free University of Brussels. Ph.D. in Computer Science from U.C. Santa Cruz. Researcher at the Los Alamos National Laboratory since 2005.
Research trends. MESUR : Metrics from Scholarly Usage of Resources. ( http://www.mesur.org ) Neno / Fhat : A Semantic Network Programming Language and Virtual Machine Architecture. ( http://neno.lanl.gov ) C D M S : Collective Decision Making Systems. ( http://cdms.lanl.gov )
What is a network? A network is a data structure that is used to connect vertices /nodes/dots by means of edges /links/lines. Networks are everywhere. Social : friendship, trust, communication, collaboration. Technological : web-pages, communication, software dependencies, circuits. Scholarly : journals, authors, articles, institutions. Natural : protein interaction, neural, food web.
The undirected network. There is the undirected network of common knowledge. Sometimes called an undirected single-relational network. e.g. vertex i and vertex j are “related”. The semantic of the edge denotes the network type . e.g. friendship network, collaboration network, etc. i j
Example undirected network. Herbert Marko Aric Ed Zhiwu Alberto Jen Johan Luda Stephan Whenzong
The directed network. Then there is the directed network of common knowledge. Sometimes called a directed single-relational network. For example, vertex i is related to vertex j , but j is not related to i . i j
Example directed network. Muskrat Bear Fish Fox Meerkat Lion Human Wolf Deer Beetle Hyena
The semantic network. Finally, there is the semantic network Sometimes called a directed multi-relational network. For example, vertex i is related to vertex j by the semantic s , but j is not related to i by the semantic s . i j s
Example semantic network. SantaFe Marko NewMexico Ryan California UnitedStates LANL livesIn worksWith cityOf originallyFrom stateOf stateOf locatedIn hasLab Cells Atoms madeOf madeOf researches Oregon southOf hasResident Arnold governerOf northOf
Google’s PageRank. PageRank Used to rank web-pages that are connected by citation (hyper-link). Note: this image was stolen off the web from somewhere.
The components to calculate a stationary probability distribution. Take a single “random walker”. Place that random walker on any random vertex in the network. At every time step, the random walker transitions from its current node to an adjacent node in the network (i.e. takes a random outgoing edge from its current node.) Anytime the random walker is at a node, increment a “times visited” counter by 1. Let this algorithm run for an “infinite” amount of time. Normalize the “times visited” counters. That is your centrality vector. a 1 0.0123
Random walker example. a c b d 0 0 0 0
Random walker example. a c b d 1 0 0 0
Random walker example. a c b d 1 0 1 0
Random walker example. a c b d 1 0 1 1
Random walker example. a c b d 1 1 1 1
Random walker example. a c b d 1 1 2 1
Random walker example. a c b d 1 2 2 1
Random walker example. a c b d 2 2 2 1
Random walker example. a c b d 2 2 3 1
Random walker example. a c b d 2 2 3 2
Random walker example. a c b d 2 3 3 2
Random walker example. a c b d 2 3 4 2
Random walker example. a c b d 66785 133310 133321 66784
Random walker example. a c b d 0.167 0.332 0.332 0.167
Breather.
Example semantic network. SantaFe Marko NewMexico Ryan California UnitedStates LANL livesIn worksWith cityOf originallyFrom stateOf stateOf locatedIn hasLab Cells Atoms madeOf madeOf researches Oregon southOf hasResident Arnold governerOf northOf
What is the Semantic Web? The figurehead of the Semantic Web initiative, Tim Berners-Lee, describes the Semantic Web as “ ... an extension of the current web in which information is given well-defined meaning, better enabling computers and people to work in cooperation. ” Perhaps not the best definition. It implies a particular application space--namely the “web metadata and intelligent agents” space. My definition is that the Semantic Web is “ a distributed, standardized semantic network data model--a URG (Uniform Resource Graph). It’s a uniform way of graphing resources. ”
What is a resource? Resource = Anything. Anything that can be identified. The Uniform Resource Identifier (URI): <scheme name> : <hierarchical part> [ ? <query> ] [ # <fragment> ] http://www.lanl.gov urn:uuid:550e8400-e29b-41d4-a716-446655440000 urn:issn:0892-3310 http://www.lanl.gov#MarkoRodriguez prefix it to make it easier on the eyes -- lanl:MarkoRodriguez The Semantic Web “ first identify it, then relate it! ”
The technologies of the Semantic Web. Resource Description Framework (RDF): The foundation technology of the Semantic Web. RDF is a highly-distributed, semantic network data model. In RDF, URIs and literals (e.g. ints, doubles, strings) are related to one another in triples. <lanl:marko> <lanl:worksWith> <lanl:jhw> <lanl:jhw> <lanl:wrote> <lanl:LAUR-07-2028> <lanl:LAUR-07-2028> <lanl:hasTitle> “Web-Based Collective Decision Making Systems”^^<xsd:string> RDF Schema (RDFS): The ontology is to the Semantic Web as the schema is to the relational database. “ Anything of rdf:type lanl:Human can lanl:drive anything of rdf:type lanl:Car .”
RDF and RDFS. lanl:marko lanl:cookie lanl:Human lanl:Food lanl:isEating rdf:type rdf:type lanl:isEating rdfs:domain rdfs:range ontology instance RDF is not a syntax. It’s a data model. Various syntaxes exist to encode RDF including RDF/XML, N-TRIPLE, TRiX, N3, etc.
PageRank in a semantic network? lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote ? lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type ? ?
Components of a grammar-based walker. A walker . Discrete element. A grammar . An abstract representation of legal path for the walker take. e.g. “you can traverse a lanl:friendOf edge from a lanl:Human to another lanl:Human .” Also includes rules: “increment a counter.”, “don’t ever return to this vertex.” A data set that respects the ontological “expectations” of the grammar.
Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 0 0 0 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.” 1 0 0
Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 1 0 0 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 1 0 1 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 1 0 1 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 2 0 1 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 2 0 1 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
Grammars create implicit relationships. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type lanl:hasCoauthor
Conclusions. Many systems can be represented as a network. The semantic network is a more expressive, though less studied data model. The grammar technique can be used to port many of the common network analysis algorithms to the semantic network domain.
Related publications. Rodriguez, M.A., Watkins, J.H., Bollen, J., Gershenson, C., “ Using RDF to Model the Structure and Process of Systems ”, International Conference on Complex Systems, Boston, Massachusetts, LAUR-07-5720, October 2007. Rodriguez, M.A., Bollen, J., Van de Sompel, H., “ A Practical Ontology for the Large-Scale Modeling of Scholarly Artifacts and their Usage ”, 2007 ACM/IEEE Joint Conference on Digital Libraries, pages 278-287, Vancouver, Canada, ACM/IEEE Computing, doi:10.1145/1255175.1255229, LA-UR-07-0665, June 2007. Rodriguez, M.A., &quot;Social Decision Making with Multi-Relational Networks and Grammar-Based Particle Swarms &quot;, 2007 Hawaii International Conference on Systems Science (HICSS), pages 39-49, Waikoloa, Hawaii, IEEE Computer Society, ISSN: 1530-1605, doi:10.1109/HICSS.2007.487, LA-UR-06-2139, January 2007. Rodriguez, M.A., &quot; A Multi-Relational Network to Support the Scholarly Communication Process &quot;, International Journal of Public Information Systems, volume 2007, issue 1, pages 13-29, ISSN: 1653-4360, LA-UR-06-2416, March 2007. Rodriguez, M.A., “ Mapping Semantic Networks to Undirected Networks ”, LA-UR-07-5287, August 2007. Rodriguez, M.A., Watkins, J.H., “ Grammar-Based Geodesics in Semantic Networks ”, LA-UR-07-4042, June 2007. Rodriguez, M.A., Bollen, J., “ Modeling Computations in a Semantic Network ”, LA-UR-07-3678, May 2007. Rodriguez, M.A., “ General-Purpose Computing on a Semantic Network Substrate ”, LA-UR-07-2885, April 2007. Rodriguez, M.A., “ Grammar-Based Random Walkers in Semantic Networks ”, Knowledge-Based Systems, Elsevier, LA-UR-06-7791, in press, 2007.
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The Network Data Structure in Computing

  • 1. The Network Data Structure in Computing Marko A. Rodriguez Los Alamos National Laboratory Vrije Universiteit Brussel [email_address] http://cnls.lanl.gov/~marko
  • 2. About me. Marko Antonio Rodriguez. Bachelors of Science in Cognitive Science from U.C. San Diego. Minor in the Arts in Computer Music from U.C. San Diego. Masters of Science in Computer Science from U.C. Santa Cruz. Visiting Researcher at the Center for Evolution, Complexity, and Cognition at the Free University of Brussels. Ph.D. in Computer Science from U.C. Santa Cruz. Researcher at the Los Alamos National Laboratory since 2005.
  • 3. Research trends. MESUR : Metrics from Scholarly Usage of Resources. ( http://www.mesur.org ) Neno / Fhat : A Semantic Network Programming Language and Virtual Machine Architecture. ( http://neno.lanl.gov ) C D M S : Collective Decision Making Systems. ( http://cdms.lanl.gov )
  • 4. What is a network? A network is a data structure that is used to connect vertices /nodes/dots by means of edges /links/lines. Networks are everywhere. Social : friendship, trust, communication, collaboration. Technological : web-pages, communication, software dependencies, circuits. Scholarly : journals, authors, articles, institutions. Natural : protein interaction, neural, food web.
  • 5. The undirected network. There is the undirected network of common knowledge. Sometimes called an undirected single-relational network. e.g. vertex i and vertex j are “related”. The semantic of the edge denotes the network type . e.g. friendship network, collaboration network, etc. i j
  • 6. Example undirected network. Herbert Marko Aric Ed Zhiwu Alberto Jen Johan Luda Stephan Whenzong
  • 7. The directed network. Then there is the directed network of common knowledge. Sometimes called a directed single-relational network. For example, vertex i is related to vertex j , but j is not related to i . i j
  • 8. Example directed network. Muskrat Bear Fish Fox Meerkat Lion Human Wolf Deer Beetle Hyena
  • 9. The semantic network. Finally, there is the semantic network Sometimes called a directed multi-relational network. For example, vertex i is related to vertex j by the semantic s , but j is not related to i by the semantic s . i j s
  • 10. Example semantic network. SantaFe Marko NewMexico Ryan California UnitedStates LANL livesIn worksWith cityOf originallyFrom stateOf stateOf locatedIn hasLab Cells Atoms madeOf madeOf researches Oregon southOf hasResident Arnold governerOf northOf
  • 11. Google’s PageRank. PageRank Used to rank web-pages that are connected by citation (hyper-link). Note: this image was stolen off the web from somewhere.
  • 12. The components to calculate a stationary probability distribution. Take a single “random walker”. Place that random walker on any random vertex in the network. At every time step, the random walker transitions from its current node to an adjacent node in the network (i.e. takes a random outgoing edge from its current node.) Anytime the random walker is at a node, increment a “times visited” counter by 1. Let this algorithm run for an “infinite” amount of time. Normalize the “times visited” counters. That is your centrality vector. a 1 0.0123
  • 13. Random walker example. a c b d 0 0 0 0
  • 14. Random walker example. a c b d 1 0 0 0
  • 15. Random walker example. a c b d 1 0 1 0
  • 16. Random walker example. a c b d 1 0 1 1
  • 17. Random walker example. a c b d 1 1 1 1
  • 18. Random walker example. a c b d 1 1 2 1
  • 19. Random walker example. a c b d 1 2 2 1
  • 20. Random walker example. a c b d 2 2 2 1
  • 21. Random walker example. a c b d 2 2 3 1
  • 22. Random walker example. a c b d 2 2 3 2
  • 23. Random walker example. a c b d 2 3 3 2
  • 24. Random walker example. a c b d 2 3 4 2
  • 25. Random walker example. a c b d 66785 133310 133321 66784
  • 26. Random walker example. a c b d 0.167 0.332 0.332 0.167
  • 28. Example semantic network. SantaFe Marko NewMexico Ryan California UnitedStates LANL livesIn worksWith cityOf originallyFrom stateOf stateOf locatedIn hasLab Cells Atoms madeOf madeOf researches Oregon southOf hasResident Arnold governerOf northOf
  • 29. What is the Semantic Web? The figurehead of the Semantic Web initiative, Tim Berners-Lee, describes the Semantic Web as “ ... an extension of the current web in which information is given well-defined meaning, better enabling computers and people to work in cooperation. ” Perhaps not the best definition. It implies a particular application space--namely the “web metadata and intelligent agents” space. My definition is that the Semantic Web is “ a distributed, standardized semantic network data model--a URG (Uniform Resource Graph). It’s a uniform way of graphing resources. ”
  • 30. What is a resource? Resource = Anything. Anything that can be identified. The Uniform Resource Identifier (URI): <scheme name> : <hierarchical part> [ ? <query> ] [ # <fragment> ] http://www.lanl.gov urn:uuid:550e8400-e29b-41d4-a716-446655440000 urn:issn:0892-3310 http://www.lanl.gov#MarkoRodriguez prefix it to make it easier on the eyes -- lanl:MarkoRodriguez The Semantic Web “ first identify it, then relate it! ”
  • 31. The technologies of the Semantic Web. Resource Description Framework (RDF): The foundation technology of the Semantic Web. RDF is a highly-distributed, semantic network data model. In RDF, URIs and literals (e.g. ints, doubles, strings) are related to one another in triples. <lanl:marko> <lanl:worksWith> <lanl:jhw> <lanl:jhw> <lanl:wrote> <lanl:LAUR-07-2028> <lanl:LAUR-07-2028> <lanl:hasTitle> “Web-Based Collective Decision Making Systems”^^<xsd:string> RDF Schema (RDFS): The ontology is to the Semantic Web as the schema is to the relational database. “ Anything of rdf:type lanl:Human can lanl:drive anything of rdf:type lanl:Car .”
  • 32. RDF and RDFS. lanl:marko lanl:cookie lanl:Human lanl:Food lanl:isEating rdf:type rdf:type lanl:isEating rdfs:domain rdfs:range ontology instance RDF is not a syntax. It’s a data model. Various syntaxes exist to encode RDF including RDF/XML, N-TRIPLE, TRiX, N3, etc.
  • 33. PageRank in a semantic network? lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote ? lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type ? ?
  • 34. Components of a grammar-based walker. A walker . Discrete element. A grammar . An abstract representation of legal path for the walker take. e.g. “you can traverse a lanl:friendOf edge from a lanl:Human to another lanl:Human .” Also includes rules: “increment a counter.”, “don’t ever return to this vertex.” A data set that respects the ontological “expectations” of the grammar.
  • 35. Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 0 0 0 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
  • 36. Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.” 1 0 0
  • 37. Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 1 0 0 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
  • 38. Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 1 0 1 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
  • 39. Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 1 0 1 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
  • 40. Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 2 0 1 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
  • 41. Grammar-based PageRank example. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type 2 0 1 “ Take only lanl:wrote out-edge to a resource of rdf:type lanl:Article . Then take a lanl:wrote in-edge to a resource of rdf:type lanl:Human . Increment only lanl:Human s. Make sure that the lanl:Human seen before is not the same lanl:Human currently. Repeat infinitely.”
  • 42. Grammars create implicit relationships. lanl:marko lanl:p1 lanl:wrote lanl:johan lanl:wrote lanl:chuck lanl:hasFriend lanl:Article rdf:type rdf:type lanl:Human rdf:type rdf:type lanl:hasCoauthor
  • 43. Conclusions. Many systems can be represented as a network. The semantic network is a more expressive, though less studied data model. The grammar technique can be used to port many of the common network analysis algorithms to the semantic network domain.
  • 44. Related publications. Rodriguez, M.A., Watkins, J.H., Bollen, J., Gershenson, C., “ Using RDF to Model the Structure and Process of Systems ”, International Conference on Complex Systems, Boston, Massachusetts, LAUR-07-5720, October 2007. Rodriguez, M.A., Bollen, J., Van de Sompel, H., “ A Practical Ontology for the Large-Scale Modeling of Scholarly Artifacts and their Usage ”, 2007 ACM/IEEE Joint Conference on Digital Libraries, pages 278-287, Vancouver, Canada, ACM/IEEE Computing, doi:10.1145/1255175.1255229, LA-UR-07-0665, June 2007. Rodriguez, M.A., &quot;Social Decision Making with Multi-Relational Networks and Grammar-Based Particle Swarms &quot;, 2007 Hawaii International Conference on Systems Science (HICSS), pages 39-49, Waikoloa, Hawaii, IEEE Computer Society, ISSN: 1530-1605, doi:10.1109/HICSS.2007.487, LA-UR-06-2139, January 2007. Rodriguez, M.A., &quot; A Multi-Relational Network to Support the Scholarly Communication Process &quot;, International Journal of Public Information Systems, volume 2007, issue 1, pages 13-29, ISSN: 1653-4360, LA-UR-06-2416, March 2007. Rodriguez, M.A., “ Mapping Semantic Networks to Undirected Networks ”, LA-UR-07-5287, August 2007. Rodriguez, M.A., Watkins, J.H., “ Grammar-Based Geodesics in Semantic Networks ”, LA-UR-07-4042, June 2007. Rodriguez, M.A., Bollen, J., “ Modeling Computations in a Semantic Network ”, LA-UR-07-3678, May 2007. Rodriguez, M.A., “ General-Purpose Computing on a Semantic Network Substrate ”, LA-UR-07-2885, April 2007. Rodriguez, M.A., “ Grammar-Based Random Walkers in Semantic Networks ”, Knowledge-Based Systems, Elsevier, LA-UR-06-7791, in press, 2007.