Detecting Community Structure in Complex Networks

HAMID SHAHRIVARI

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Outlines

I. Definition of Complex Networks

II. Definition of Community Structure

III. Various Approaches for Detection of Community Structure

IV. Evaluating the Quality of Community Structure

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Definition of Complex Networks

Collection of nodes betwhich edges explain nodes’ relation

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Definition of Community Structure

Sub-graph in which the edges inside it are denser than edges between sub-graph and rest of the network

Identifying optimum separation is NP-Complete

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Different Type of Community Structure

Overlapping Disjoint

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Usage

Apprehend the

Structure of Networks

Improvement of Semantic

Analysis

Drawing the

Network

Identifying

Similar Entities

Improvement of Search Engine

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Approaches

Heuristic

Divisive

Agglomerative

Optimization

Meta Heuristic

Approximation

Random

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Accuracy

Speed

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Girvan-Newman Algorithm

Heuristic

Divisive

Flexible and Accurate

High Complexity

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Calculate edge betweenness of all

edges

Remove the edge possessing most edge

betweenness value

Is network divided

Does each part satisfy community structure

criteria?

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Label Propagation Algorithm

Random-based

Liner Time Complexity

Low Accuracy

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Evaluation

Real World Networks

Modeled from Real Problems

Various Structure

Unknown Ideal Answer

Artificial Networks

Generated by Machines

Similar Structure

Containing Ground Truth

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Artificial Network LFR

Generates networks in liner time

Capable of generating various size network

Obtaining Power Law

Could determine the number and size of community structure

Generate graph with different level of community structure obviousity

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Evaluation Metrics

ModularityReal World Network

• Edges inside community possess positive value

• Edges between two communities possess negative value

• Result ranges between -0.5 to 1

Normalized Mutual InformationArtificail Network

• Defines how much detected community structures overlaps ground truth community structures

• Results ranges between 0 to 1

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