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 [soon].
o I defend November 15, 2007!
• Researcher at the Los Alamos National Laboratory since 2005.

Marko A. Rodriguez

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)

• CDMS: Collective Decision Making Systems. (http://cdms.lanl.gov)

Marko A. Rodriguez

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.
o Social: friendship, trust, communication, collaboration.
o Technological: web-pages, communication, software dependencies, circuits.
o Scholarly: journals, authors, articles, institutions.
o Natural: protein interaction, neural, food web.

Marko A. Rodriguez

The undirected network.

• There is the undirected network of common knowledge.
o Sometimes called an undirected single-relational network.
o e.g. vertex i and vertex j are “related”.

• The semantic of the edge denotes the network type.
o e.g. friendship network, collaboration network, etc.

i j

Marko A. Rodriguez

Example undirected network.

Jen
Alberto Whenzong

Luda
Aric
Herbert Zhiwu

Ed

Johan
Stephan
Marko

Marko A. Rodriguez

The directed network.

• Then there is the directed network of common knowledge.
o Sometimes called a directed single-relational network.
o For example, vertex i is related to vertex j, but j is not related to i.

i j

Marko A. Rodriguez

Example directed network.

Human
Lion Hyena

Deer
Fish
Muskrat Meerkat

Fox

Wolf
Beetle
Bear

Marko A. Rodriguez

The semantic network.

• Finally, there is the semantic network
o Sometimes called a directed multi-relational network.
o 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

Marko A. Rodriguez

Example semantic network.

LANL hasLab
UnitedStates Arnold
researches
locatedIn stateOf
stateOf governerOf
Atoms
cityOf NewMexico
SantaFe California

madeOf hasResident originallyFrom
Ryan northOf
livesIn southOf
Cells madeOf worksWith
Oregon
Marko

Marko A. Rodriguez

What are the techniques for analysis?

• Degree statistics
o How many in- and out-edges does vertex i have?
o What is the maximum and minimum in- and out-degree of the network?

• Shortest-path metrics
o What is the smallest number of steps to get from vertex i to vertex j?
o How many of the shortest-paths go through vertex i?

• Power metrics
o What vertices are the most “influential”?

• Metadata distributions
o What is the probability that a vertex of type x is connected to a vertex of type y?

Marko A. Rodriguez

Degree statistics. Max_out = 4
Max_in = 4
Min_out = 0
out = 2
Min_in = 0
in = 1 out = 3
Human in = 0
out = 1
Lion Hyena
in = 0
out = 0
in = 2 out = 0
out = 1 in = 4
Deer in = 1
Fish out = 1
Muskrat Meerkat
in = 3

out = 1 Fox
in = 1
out = 1
Wolf out = 0
in = 1 Beetle
in = 1
Bear out = 4
in = 0

Marko A. Rodriguez

Shortest-path between Marko and Aric.

Jen
Alberto Whenzong

Luda
Aric
Herbert Zhiwu

Ed

Johan
Stephan
Marko
Shortest path = 1

Marko A. Rodriguez

Eccentricity of Marko.

Jen
Alberto Whenzong

Luda
Aric
Herbert Zhiwu

Ed

Johan
Stephan
Marko
Eccentricity = 3

Marko A. Rodriguez

Radius of the network.

Jen
Alberto Whenzong

Luda
Aric
Herbert Zhiwu

Ed

Johan
Stephan
Marko
Radius = 3

Marko A. Rodriguez

Diameter of the network.

Jen
Alberto Whenzong

Luda
Aric
Herbert Zhiwu

Ed

Johan
Stephan
Marko
Diameter = 4

Marko A. Rodriguez

Closeness of Marko.

Jen
Alberto Whenzong

Luda
Aric
Herbert Zhiwu

Ed

Johan
Stephan
Marko
Closeness = 0.0526

Marko A. Rodriguez

Shortest-path metrics.

Shortest-path Eccentricity

Radius Diameter

Closeness Betweenness

Marko A. Rodriguez

Power metrics.

• Eigenvector Centrality
o Rank vertices according to the primary eigenvector of the adjacency matrix
representing the network.
o In the language of Markov chains, find the stationary probability distribution of the
chain.

• PageRank
o Ensure a real-valued ranking by introducing a “teleportation-network” which
ensures strong connectivity (used by Google).

Marko A. Rodriguez

The components to calculate a
stationary probability distribution.

• Take a single “random walker”.

• Place that random walker on any random vertex in the network. a

• 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. 1

• Let this algorithm run for an “infinite” amount of time.

• Normalize the “times visited” counters.
o That is your centrality vector. 0.0123

Marko A. Rodriguez

Random walker example.

b 0

0 a

d 0

0 c

Marko A. Rodriguez


b 0

1 a

d 0

0 c

Marko A. Rodriguez


b 1

1 a

d 0

0 c

Marko A. Rodriguez


b 1

1 a

d 1

0 c

Marko A. Rodriguez


b 1

1 a

d 1

1 c

Marko A. Rodriguez


b 2

1 a

d 1

1 c

Marko A. Rodriguez


b 2

1 a

d 1

2 c

Marko A. Rodriguez


b 2

2 a

d 1

2 c

Marko A. Rodriguez


b 3

2 a

d 1

2 c

Marko A. Rodriguez


b 3

2 a

d 2

2 c

Marko A. Rodriguez


b 3

2 a

d 2

3 c

Marko A. Rodriguez


b 4

2 a

d 2

3 c

Marko A. Rodriguez


b 133321

66785 a

d 66784

133310 c

Marko A. Rodriguez


b 0.332

0.167 a

d 0.167

0.332 c

Marko A. Rodriguez

PageRank.

• The random walker has 0.85 probability of using G as its propagation network
and a 0.15 probability of using H as its propagation network (Google’s published
alpha value).
• Every node is reachable by every other node and thus, is strongly connected.
• A strongly connected network guarantees a stationary probability distribution.

Marko A. Rodriguez

Metadata distribution metrics.

• Scalar Assortativity
o What’s the probability of encountering a node with degree x?
o What’s the probability of encountering a node with degree x that is
connected to a node of degree y?
o What’s the probability of encountering a node with degree x that is
connected to a node of degree y that is connected to a node of degree z?
o …

• Discrete Assortativity
o What’s the probability of encountering a node with metadata x?
o What’s the probability of encountering a node with metadata x that is
connected to a node of metadata y?
o What’s the probability of encountering a node with metadata x that is
connected to a node of metadata y that is connected to a node of metadata
z?
o …

Marko A. Rodriguez

The CENS network dataset.

• Center for Embedded Network Sensing at U.C. Los Angeles.
• “An interdisciplinary and multi-institutional venture, CENS involves hundreds of
faculty, engineers, graduate student researchers, and undergraduate students
from multiple disciplines at the partner institutions of University of California at
Los Angeles (UCLA), University of Southern California (USC), University of
California Riverside (UCR), California Institute of Technology (Caltech),
University of California at Merced (UCM), and California State University at Los
Angeles (CSULA).”

Marko A. Rodriguez

Everything is metadata.

Affilation LANL
Department Research Library
Gender Male
JobRank Ph.D. Student
Buidling P362
Lab Prototyping Team
Advisor Johan Bollen
Degree 2

Marko

…. ….

Marko A. Rodriguez

The CENS coauthorship network.

• UCLA - red
• USC - orange
• Coventry - green
• …

• Ph.D. - ellipse
• Professor - hexagon
• …

Marko A. Rodriguez

1st-order degree distributions in CENS coauthorship network.

Marko A. Rodriguez

2nd-order degree distributions in CENS coauthorship network.

Marko A. Rodriguez

2nd-order degree assortativity in CENS coauthorship network.

• Pearson correlation on edge degrees.
o r in [-1,1]

• r = 0.212

Marko A. Rodriguez

2nd-order degree assortativity in other networks.

• Physics coauthorship: 0.363
• Biology coauthorship: 0.127
• Mathematics coauthorship: 0.120
• Film actor collaborations: 0.208

• Internet: -0.189
• World Wide Web: -0.065

• Neural network: -0.163
• Marine food web: -0.247

• Random graph: 0.0
• Regular graph: 1.0

Newman, M.J., “Assortative Mixing in Networks”, Physical Review Letters, 89(20), 2002.

Marko A. Rodriguez

Metadata path frequencies.
• 1064.0 UCLA UCLA • 376.0 Phd Professor
• 442.0 USC USC • 254.0 Phd Researcher
• 336.0 USC UCLA • 242.0 Researcher Professor
• 76.0 MIT UCLA • 184.0 Phd Phd
• 58.0 UCLA UCM
• 142.0 Professor Professor
• 32.0 Caltech UCLA

• 1186.0 Male Male • 304.0 US US
• 508.0 Male Female • 156.0 India US
• 78.0 Female Female • 70.0 India India
• 58.0 US China
• 750.0 CS CS • 36.0 India China
• 388.0 EE CS • 28.0 China China
• 340.0 EE EE • 24.0 US Italy
• 84.0 CS CivilEng • 18.0 Iran India
• 78.0 Biology CS • 14.0 Iran US
• 74.0 CivilEng CivilEng • 12.0 Greece India

Marko A. Rodriguez

2nd-order metadata assortativity in CENS coauthorship
network.

• 0.696 Gender
• 0.641 Affiliation
• 0.513 Department
• 0.482 Advisor
• 0.426 Lab
• 0.319 Building
• 0.290 Origin
• 0.168 JobRank
• 0.042 Room

Marko A. Rodriguez

3rd-order metadata assortativity in CENS coauthorship
network.

• 0.471 Gender
• 0.435 Affiliation
• 0.290 Department
• 0.225 Origin
• 0.207 Advisor
• 0.195 Lab
• 0.170 Building
• 0.032 JobRank
• 0.004 Room

Marko A. Rodriguez

Metadata compression.

• 229.0 US:Male US:Female
• 228.0 US:Male US:Male
• 197.0 US:Male India:Male
• 121.0 India:Male India:Male
• 76.0 India:Male US:Female
• 36.0 US:Male China:Male
• 30.0 US:Female US:Female
• 21.0 Taiwan:Male China:Male
• 19.0 US:Male Italy:Male
• 18.0 India:Male South Korea:Male
• 17.0 India:Male China:Male
• 17.0 India:Male Australia:Male
• 16.0 China:Male China:Male
• 16.0 India:Male Greece:Male
• 16.0 US:Male Mexico:Male

Marko A. Rodriguez

3rd-order metadata compression.

• 1402.0 UCLA:Phd UCLA:Professor UCLA:Phd
• 879.0 UCLA:Researcher UCLA:Professor UCLA:Phd
• 605.0 UCLA:Professor UCLA:Professor UCLA:Phd
• 512.0 UCLA:Researcher UCLA:Professor UCLA:Researcher
• 380.0 UCLA:Researcher UCLA:Professor UCLA:Professor
• 304.0 USC:Phd UCLA:Professor UCLA:Phd
• 294.0 USC:Phd USC:Professor USC:Phd
• 272.0 UCLA:Phd UCLA:Phd UCLA:Phd
• 270.0 UCLA:Professor UCLA:Phd UCLA:Phd

Marko A. Rodriguez

Breather.

Marko A. Rodriguez

What is the Semantic Web?

• The figurehead of the Semantic Web initiative, Tim Berners-Lee, describes the
Semantic Web as
o “... 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
o “a highly-distributed, standardized semantic network data model--a URG (Uniform
Resource Graph). It’s a uniform way of graphing resources.”

Marko A. Rodriguez

What is a resource?

• Resource = Anything.
o Anything that can be identified.

• The Uniform Resource Identifier (URI):
o <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
o “first identify it, then relate it!”

Marko A. Rodriguez

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.
o <lanl:marko> <lanl:worksWith> <lanl:jhw>
o <lanl:jhw> <lanl:wrote> <lanl:LAUR-07-2028>
o <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.
o “Anything of rdf:type lanl:Human can lanl:drive anything of rdf:type lanl:Car.”

• Triple-Store: The triple-store is to semantic networks what the relational
database is to the data table.
o a.k.a. semantic repository, graph database, RDF database.

Marko A. Rodriguez

RDF and RDFS.

lanl:Human lanl:Food
rdfs:range
rdfs:domain

lanl:isEating
ontology rdf:type rdf:type

instance
lanl:isEating
lanl:marko lanl:cookie

RDF is not a syntax. It’s a data model. Various syntaxes exist to encode RDF including RDF/XML, N-TRIPLE, TRiX, N3, etc.

Marko A. Rodriguez

The triple-store.

• There are two primary ways to distribute information on the Semantic Web.
o 1.) publish RDF/XML document on a web server.
o 2.) expose a public interface to an RDF triple-store.
• The triple store is to semantic networks what the relational database is to data
tables.
o Storing and querying triples in a triple store.
o SPARQLUpdate query language.
- like SQL, but for triple-stores.

SELECT ?a ?c WHERE INSERT ?a coauthor ?c WHERE
{ ?a type human { ?a type human
?a wrote ?b ?a wrote ?b
?b type article ?b type article
?c wrote ?b ?c wrote ?b
?c type human ?c type human
?a != ?c } ?a != ?c }

DELETE ?s ?p ?o WHERE { ?s ?p ?o }

Marko A. Rodriguez

Triple-store vs. relational database.

Triple-store Relational Database

SPARQL Interface SQL Interface

SELECT (?x4) SELECT collaboratesWithTable.ordId2
WHERE { FROM personTable, authorTable, articleTable, friendTable,
hasEmployeeTable, organizationTable, worksForTable,
?x1 dc:creator lanl:LAUR-06-2139. collaboratesWithTable
?x1 lanl:hasFriend ?x2 . WHERE
?x2 lanl:worksFor ?x3 . personTable.id = authorTable.personId AND
?x3 lanl:collaboratesWith ?x4 . authorTable.articleId = "dc:creator LAUR-06-2139" AND
?x4 lanl:hasEmployee ?x1 . } personTable.id = friendTable.personId1 AND
friendTable.personId2 = worksForTable.personId AND
worksForTable.orgId = collaboratesWithTable.orgId2 AND
collaboratesWithTable.ordId2 = personTable.id

Marko A. Rodriguez

Semantic network metrics?

• What does it means to run a shortest-path calculation on a semantic network?
o Shortest-path along which semantic--which edge type(s)?

• What does it mean to calculate PageRank on a semantic network?
o What are legal semantics for the random walker?

Marko A. Rodriguez

Shortest-path metrics in a semantic network?

lanl:hasFriend
lanl:marko lanl:johan
lanl:hasFriend
lanl:hasFriend
lanl:livesInSameCityAs

lanl:chuck
lanl:bob

lanl:hasFriend
lanl:jill

“What is the shortest path between lanl:marko and lanl:jill by taking only lanl:hasFriend edges?”

Marko A. Rodriguez

PageRank in a semantic network?

lanl:Human lanl:Article
rdf:type
rdf:type

rdf:type rdf:type
lanl:p1

lanl:wrote
lanl:wrote
?

?
?

lanl:hasFriend

lanl:chuck

Marko A. Rodriguez

Grammar-based geodesics and random walkers.

• How do you port many of the undirected and directed single-relational network
analysis algorithms over to the semantic network domain?
o My solution is what I call a grammar.

• Nearly every network analysis algorithm can be represented in terms of a walker
traversing a network.
o Geodesics.
o PageRank
o Metadata paths.
o etc.

Marko A. Rodriguez

Components of a grammar-based walker.

• A walker.
o Discrete element.

• A grammar.
o 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.

Marko A. Rodriguez

Grammar-based PageRank example.

rdf:type
rdf:type

rdf:type rdf:type
lanl:p1

lanl:wrote
lanl:wrote

lanl:marko 0 lanl:johan 0

lanl:hasFriend “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:Humans. Make sure that the
lanl:chuck 0 lanl:Human seen before is not the same
lanl:Human currently. Repeat infinitely.”

Marko A. Rodriguez


rdf:type
rdf:type

rdf:type rdf:type
lanl:p1

lanl:wrote
lanl:wrote



Marko A. Rodriguez

Grammars create implicit relationships.

rdf:type
rdf:type

rdf:type rdf:type
lanl:p1

lanl:wrote
lanl:wrote

lanl:hasCoauthor
lanl:hasFriend

lanl:chuck

Marko A. Rodriguez

Conclusions.

• Many data sets can be represented as a network of “actors”.
• There exists many network analysis algorithms.
o Shortest-path metrics.
o Eigenvector-based metrics.
o Assortativity coefficients.

• The semantic network data structure is a less studied data model.
o Semantic Web community doesn’t take a network approach to their substrate.

• The grammar technique can be used to port many of the common network
analysis algorithms to the semantic network domain.
o Grammar-based geodesics.
o Grammar-based random walkers.

Marko A. Rodriguez

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., "Social Decision Making with Multi-Relational Networks and Grammar-Based
Particle Swarms", 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., "A Multi-Relational Network to Support the Scholarly Communication Process",
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”, LA-UR-06-7791, November
2006.

Marko A. Rodriguez

The Network: A Data Structure that Links Domains

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