Metric Measurement of the Network Graph

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Metric Measurement of the Network Graph

• Genie Hsieh
• May 6, 2004

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Background

• The oldest studies of the large-scale statistical
  properties of networks are the studies of social
  networks.
• Complex networks describes a wide range of
  systems in nature and society.
• Many networks might possess community structure.
• In community structure, network vertices and
  others that are like them in some way have
  preferential association.

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Complex Networks
Sociology

• Statistics

Computer networking
Discrete Math -graph theory -group theory -matrix
algebra
NETWORK ANALYSIS
Epidemiology
Biology

• Social Networks
• Vertices individuals edges relationship
• Technology Networks
• Vertices routers/computers edges
  physical/wireless links
• Biological Networks
• Vertices protein edges interactions

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Analyze clustering of gold probes

• Why?
• Derive biological important information for the
  modeling of transduction pathways.
• Sheets of cell membrane labeled with gold probe
  is used to characterize distributions of
  receptors, signaling proteins and liquids.
• The first step in signaling is ligand binding to
  membrane receptors which initiates cascades of
  biochemical events leading to physiological
  responses.

Transmission Electron Microscopy
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Statistical Thread-Hopkins

• The Hopkins statistic tests spatial randomness by
  comparing nearest-neighbor distances from random
  points and randomly chosen probes.

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Statistical Approach-Weakness

• Do not know community structures.
• Cannot show the relationship between any two
  vertices in a cluster.

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Computer Science Thread-NewmanGirvan

• Algorithm
• Calculate the edge betweenness of every edge in
  the network
• Remove the edge with the highest betweenness
  score.
• Recalculate betweenness scores on the resulting
  network and repeat step 2until no edges remain.
• Betweenness the number of shortest paths between
  pairs of vertices that pass through that
  actor/edge. i.e. to measure centrality of the
  actor.
• Edges are replaced at random between vertices
  with probabilities.

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What I modified

• What does the edge represent?
• Distance between any two vertices.
• If Dist(V1,V2) lt threshold, then place edge
  between V1 and V2.
• How to show the characteristics of within a
  cluster
• Add attribute weight to every edge
• Weight (1 distance/average distance) 10
• The higher the weight, the larger the force
  connecting the two vertices.

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2D view of the Network
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Output- 25 clusters
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Output- 35 clusters
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Conclusion and Future Work

• Networking method shows intra-cluster and
  inter-cluster relationships in the network.
• Calculate similarity/dissimilarity among
  different community structures.
• Try other clustering algorithms
• Be able to compare the performances of different
  clustering approach
• Homogeneity intra-cluster measure
• Separation inner-cluster measure