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Understanding Complex Systems through Network Science

**Introduction**

We live in a time where everything we do is tagged by data. Data is not only available for individuals but also for universal and biological existence. However, with the increase in data, complexity increases. Biological existence is governed by a complicated genetic and molecular network, while society is not simply a sum of individuals, rather it is the interactions among them that make the society work.

**Mapping Complex Systems**

To understand complex systems, we need to map out their architecture and the network behind them. Data offers a unique laboratory for scientists to understand the working of the world. Graph theory emerged as a prominent subject of study for mathematicians.

Mid-1959 and 1960 were windows of time where they published eight papers that put down the ‘theory of random graphs.’ They looked at complex networks around us and said, for all practical purposes, they seem random. With such thoughts in mind, they built what we call today a ‘random network model.’

**The Physics of Random Networks**

For physicists, randomness does not mean unpredictability. Randomness is a source of predictability. Erdős and Rényi proved that in a random network, the average dominates. A typical person has about a thousand people they know on a first-name basis. The random model suggests that the most popular person should have about 1,150 friends, and the least popular person should have around 850 friends, indicating a Poisson-like distribution.

**The Rise of Network Science**

Years of being interested in networks led to the need for real data that describes real networks. The map of the world wide web was the first opportunity to study actual networks, and that marked the beginning of what we call today, ‘network science.’ We realized that the degree distribution did not follow the Poisson that we had for a random network. It followed a Power law distribution, which we later named ‘scale-free networks.’

**Growth and Preferential Attachment**

Real networks grow by starting with one node and continuously adding other nodes. The concept of ‘preferential attachment’ formalizes our connection pattern, which is biased towards the more nodes. Growth and preferential attachment together give rise to power laws, and we have hubs, as we saw earlier in the world wide web.

**Conclusion**

Network science is a necessary path if we want to understand complex systems that emerge from the interaction of many components. Today, we have network science that describes all of them within one scientific framework.

**FAQs**

**What is network theory?**

Network theory is the study of how interrelationships exist between objects or people. It provides a tool for analyzing complex systems by mapping out their relationships and examining their properties.

**What is a random network model?**

A random network model is a model in which various connections are randomly created between nodes. In this model, nodes are connected based on a probability distribution.

**What are scale-free networks?**

Scale-free networks are networks in which the distribution of nodes’ degrees follows a power law, indicating that a few nodes have many connections, while many nodes have only a few connections.

**What is preferential attachment?**

Preferential attachment is the tendency of new nodes to connect to existing nodes that already have many connections. This effect strengthens the importance of highly connected hubs in a network.

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