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Understanding complex networks

By K. Ramachandran

Dr. Venkat Venkatasubramanian — Photo: M. Moorthy

CHENNAI, AUG. 10. The science of complex networks — natural or artificial — their properties, the way they emerge and adapt themselves to their environment is the subject of a theory which was proposed recently by a group of scientists at Purdue University in the United States.

The theory seeks to lay a framework for understanding how complex networks evolve and emerge, and how they can be designed and analysed.

Natural emergence

"Our theory (published two months ago) is general but applicable for a wide variety of self-organising complex systems," says Venkat Venkatasubramanian of the Laboratory for Intelligent Process Systems (LIPS) in the Purdue University's School of Chemical Engineering.

He has co-authored the paper along with other researchers Santhoji Katare, Priyan R. Patkari and Fang-ping Mu of LIPS.

According to the theory, a complex system optimises its network structure in order to maximise its overall survival fitness.

This will in turn depend on three critical measures: efficiency, robustness and cost, and the environmental selection pressure of the network. Depending upon the extent of requirement of any of these critical measures, the networks emerge naturally in one or the other form.

`Networks will rule'

Explaining the theory, Dr. Venkatasubramanian told The Hindu recently: "The 21st century science and technology was, and would continue to be, dominated by theories for understanding, analysing and controlling large-scale networks.

"In computing it's the Internet, in the food or manufacturing industry it's the supply chain management, in power supply the distribution networks and within the human body, complex networks for food processing and signal transmission to the brain. At the nano-scale even within a single cell, there is a metabolic network or protein network."

"These networks seem different, but they share some abstract commonalities, such as nodes and connections. They adapt to environments in which they work, they change, renew, strengthen themselves or weaken.

Nonlinear

"More importantly, networks are nonlinear. They are more than the sum total of their parts. A cell or a neuron behaves in one way individually. But when a large number gather to form a network, they work completely differently. For example, our brain has 10 billion neurons and billions of connections. Individually they have certain qualities but they are unconscious of the whole. But a network of a billion connections suddenly transforms the brain and gives it self-consciousness. The emergence of this new quality is an outstanding feature of study in the 21st century... " Dr. Venkatasubramanian says.

A general conceptual framework for self-organisation of a network by evolutionary adaptation is the subject of the paper.

The network's objective is to maximise its chances of overall survival by adapting its configuration according to the environmental pressure.

Need-based adaptation

Networks adapt themselves to the environment depending on whether they need to perform efficiently, or become robust (to combat attacks or failures) or optimise cost.

For instance, the star-formation topology is commonly found in computer networks that are often designed for high-efficiency and for robustness to random failures. But the star formation is also well-known for its vulnerability to attack or failure at its central node, i.e. in the "worst case" scenario. In biological networks, this topology is found rarely but found in circles.

"Interestingly the hub-and-spokes model formation is quite prevalent in human engineered systems such as in the layout of airports, shopping malls, and other such large complex structures."

Unifying principle

In essence, the theory seems to be able to suggest when and why the different network structures might emerge, Dr. Venkatsubramanian says.

He feels that the ubiquitous presence of star, hub, and circle topologies in diverse applications seems to suggest an underlying universality concept.

That is, these topological features are independent of the details of the domain-specific mechanisms, but are governed by some unifying organisation principles.

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