A Brief Overview on Some
Recent Study of Graph Data
Yunkai Liu, Ph. D.,
Gannon University
Outlines
• Graph Database vs. Traditional Database
– Data structure
– Some frequently-used measurements
– Overview of Graph Databases
• Graph Data on Social Networks
– Case study
• Graph Data on Biology
– Case study
• Graph Data on other areas
What is the specialty of graph data in
application
• Basic Data Structure
– G = (N, E)
• Sometime edges are also named as links
• Some difference / limitation
–
–
–
–
Directed graph
Contains a large amount of attribute categories in nodes
Contains limited amount of attributes categories in edges
Rarely using adjacent matrices; hash table and indices are
widely used
• Example – SN between us
Some frequently-addressed graph
properties
• Homophily is the tendency to relate to people
with similar characteristics (status, beliefs, etc.)
– It leads to the formation of homogeneous groups
(clusters) where forming relations is easier
– Extreme homogenization can act counter to
innovation and idea generation (heterophilyis thus
desirable in some contexts)
– Homophilousties can be strong or weak
Some frequently-addressed graph
properties
• Transitivity is a property of ties: if there is a tie
between A and B and one between B and C, then
in a transitive network A and C will also be
connected
– Strong ties are more often transitive than weak
ties; transitivity is therefore evidence for the
existence of strong ties (but not a necessary or
sufficient condition)
– Transitivity and homophily together lead to the
formation of cliques (fully connected clusters)
– How to decide reasonable transitivity degree in
graph models?
Some frequently-addressed graph
properties
• Bridges are nodes and edges that connect
across groups
– Facilitate inter-group communication, increase
social cohesion, and help spur innovation
– They are usually weak ties, but not every weak tie
is a bridge
Some frequently-addressed graph
properties -Degree centrality
• A node’s (in-) or (out-)degree is the number of
links that lead into or out of the node
• In an undirected graph they are of course
identical
• Often used as measure of a node’s degree of
connectedness and hence also influence and/or
popularity
• Useful in assessing which nodes are central with
respect to spreading information and influencing
others in their immediate ‘neighborhood’
Some frequently-addressed graph
properties -Paths
• A path between two nodes is any sequence of
non-repeating nodes that connects the two
nodes
• The shortest path between two nodes is the
path that connects the two nodes with the
shortest number of edges (also called the
distance between the nodes)
– All shortest paths
– K-th shortest path
Some frequently-addressed graph
properties – Betweeness centrality
• The number of shortest paths that pass
through a node divided by all shortest paths in
the network
• Sometimes normalized such that the highest
value is 1
• Shows which nodes are more likely to be in
communication paths between other nodes
• Also useful in determining points where the
network would break apart.
Some frequently-addressed graph
properties – Closeness centrality
• The mean length of all shortest paths from a
node to all other nodes in the network (i.e. how
many hops on average it takes to reach every
other node)
• It is a measure of reach, i.e. how long it will take
to reach other nodes from a given starting node
• Useful in cases where speed of information
dissemination is main concern
• Lower values are better when higher speed is
desirable
Some frequently-addressed graph
properties – Eigenvector centrality
• A node’s eigenvector centrality is proportional to
the sum of the eigenvector centralities of all
nodes directly connected to it
• In other words, a node with a high eigenvector
centrality is connected to other nodes with high
eigenvector centrality
• This is similar to how Google ranks web pages:
links from highly linked-to pages count more
• Useful in determining who is connected to the
most connected nodes
Others measurements
• Reciprocity (degree of)
– The ratio of the number of relations which are
reciprocated (i.e. there is an edge in both
directions) over the total number of relations in
the network
– A useful indicator of the degree of mutuality and
reciprocal exchange in a network, which relate to
social cohesion
– Only makes sense in directed graphs
Others measurements
• Density
– A network’s density is the ratio of the number of edges in
the network over the total number of possible edges
between all pairs of nodes (which is n(n-1)/2, where n is
the number of vertices, for an undirected graph)
– It is a common measure of how well connected a network
is (in other words, how closely knit it is) –a perfectly
connected network is called a clique and has density=1
– A directed graph will have half the density of its undirected
equivalent, because there are twice as many possible
edges, i.e. n(n-1)
– Density is useful in comparing networks against each
other, or in doing the same for different regions within a
single network
Others measurements
• Clustering
– A node’s clustering coefficient is the density of its
neighborhood(i.e. the network consisting only of
this node and all other nodes directly connected
to it)
– The clustering coefficient for an entire network is
the average of all coefficients for its nodes
– Clustering indicative of the presence of different
(sub-)communities in a network
Others measurements
• Average and longest distance
– The longest shortest path (distance) between any two
nodes in a network is called the network’s diameter
– It also indicates how long it will take at most to reach
any node in the network (sparser networks will
generally have greater diameters)
– The average of all shortest paths in a network is also
interesting because it indicates how far apart any two
nodes will be on average (average distance)
What is Graph Database
• Graph database started in 1970s
• It is growing fast recently due to the
development of computer science tech.
– Some GD claimed that they can represent millions
of nodes and billions of edges
• GD is a part of NoSQL database
Social Network Analysis (SNA)
• News
– In 2013 Feb, Facebook announced their new “graph
search” app
• Major questions
– Networks: How to represent various social networks
– Tie Strength: How to identify strong/weak ties in the
network
– Key Players: How to identify key/central nodes in network
– Cohesion: How to characterize a network’s structure
• Major application
–
–
–
–
Social study
National security
Micro-advertisement
…
Some of my project
• Meth-Hunter
• Graph Data Management system
• Graph Data warehouse protocol
NodeXL - emails
NodeXL - Facebook
Graph Metric
Graph Type
Value
Undirected
Vertices
67
Unique Edges
Edges With Duplicates
Total Edges
165
0
165
Self-Loops
Reciprocated Vertex Pair Ratio
Reciprocated Edge Ratio
Connected Components
Single-Vertex Connected Components
Maximum Vertices in a Connected Component
Maximum Edges in a Connected Component
Maximum Geodesic Distance (Diameter)
Average Geodesic Distance
Graph Density
Modularity
0
Not Applicable
Not Applicable
8
0
29
102
4
1.878997
0.074626866
0.564555
Graph Data in Biology
• Multiple classes of bionetwork models exist, such
as metabolic, protein-gene, or protein-protein
interactions
– Metabolic networks entail nodes as metabolites and
edges as enzymes facilitating a specific reaction within
the body or nature.
– Protein-gene interactions involve understanding and
mapping gene expression.
– As with metabolic and gene expression, proteinprotein interaction networks include nodes as
proteins
Graph Data in Biology
• The structure of bio-network is important for
us to understand the nature
• The analysis part is similar with SNA,
– The clique-finding is important and it may related
with tumar.
One case study – bionetwork
alignment
• Two previous models include Graemlin
(General and robust alignment of multiple
large interaction networks) and PHUNKEE
(Pairing subgrapHs Using NetworK
Environment Equivalence)
– As Graemlin considers the entire network
spectrum, the PHUNKEE algorithm considers only
the most conserved portions between two graphs
One case study – bionetwork
alignment
• Graemlin was advantageous in that it could align
multiple networks at a fast pace, however; all
nodes and edges are considered whether or not
they are similar to each other.
• On the contrary, PHUNKEE considers only the
most conserved portions of two graphs, taking
into account that insertions and deletions may
occur over time. However, the algorithm
performs slowly, working in a step-by-step
manner.
One case study – bionetwork
alignment
• we realized that one method is not enough to
determine the relationship between two
graphs because of various factors from data.
Thus, we create a comprehensive package for
pairwise graph comparison.
– The package includes two interfaces; one is for
global alignment and another for local alignment.
– Transitivity property is also considered in case of
missing nodes or missing edges.
The bionetworks of four species in our
experiment.
Rattus
norvegicus
Mus Saccharomyces
musculus
cerevisiae
Homo
sapiens
Number of
Nodes
1212
3214
4906
11713
Number of
Edges
241746
343605
383008
1332225
The comparisons between three
species and Homo sapiens.
Rattus norvegicus
vs
Homo sapiens
Mus musculus vs
Homo sapiens
Saccharomyces
cerevisiae
vs
Homo sapiens
1124 (92.74%)
2928 (91.10%)
537(10.94%)
23233(9.61%)
17422 (5.07%)
1308(0.34%)
0.6461
-0.9850
0.8816
-0.8877
0.9045
-0.9978
Left Global Similarity
Biased on the Three
Species
0.4158
0.5616
-0.9771
Left Global Similarity
Biased on Home
sapiens
-0.9848
-0.8824
-0.9959
Number of Shared
Nodes
Number of Shared
Edges
Inner Global
Similarity
Outer Global
Similarity
A Cladogram for Rattus norvegicus,
Mus musculus and Saccharomyces
cerevisiae
Some Weird Part
• The normalization of the data is a big
challenge. It is easy to get a wrong conclusion,
which is yeast is more close to human than
mice.
• It is just an example of graph mining in
bioinformatics
Other area of Graph Data
• GIS
• Financial / business
– Public spending
• Gaming
• Some challenges of GD in CS
– Cloud app and cloud computing
– Visualization
– Integrating with other databases