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What are the most effective ways to model complex networks?

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Complex networks are ubiquitous in many fields, such as social sciences, engineering, biology, and computer science. They can represent systems of interacting agents, components, or data points, and reveal patterns, dynamics, and functions that are otherwise hidden. But how can you model complex networks effectively and efficiently? In this article, you will learn about some of the most common and powerful methods to represent, analyze, and optimize complex networks using operations research techniques.

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1 Graph Theory

One of the most fundamental and widely used ways to model complex networks is graph theory. A graph is a mathematical object that consists of a set of nodes (or vertices) and a set of edges (or links) that connect pairs of nodes. Nodes can represent entities, such as people, machines, or genes, and edges can represent relationships, such as friendship, communication, or interaction. Graphs can capture the structure and properties of complex networks, such as the degree distribution, the clustering coefficient, the diameter, and the centrality measures. Graph theory provides a rich set of tools and algorithms to explore, manipulate, and solve problems on graphs, such as finding shortest paths, spanning trees, cliques, communities, and network flows.

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Himadri Sen Gupta

PhD Candidate | Community Resilience | Natural Hazards | Optimization | Machine Learning
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Think of a complex network like a big web or puzzle of connections. To model it, you basically draw out all the pieces (we call them nodes) and how they connect to each other (those are the edges). You start by figuring out what the pieces are and how they're linked. Then, with some cool computer tools like NetworkX or Gephi, you can see which pieces are super important or find groups that are closely connected. You can even play around and see what might happen if you change things up in the web. It's like mapping out a big, interconnected city and understanding how everything works together!

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Nikolaos A. Papanikolaou

Associate Professor of Biological Chemistry, Aristotle University of Thessaloniki School of Medicine,Thessaloniki, Macedonia, Greece and Touro University, New York USA
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Graph theory is a powerful tool for modeling and analyzing biological networks, which are used to represent various biological systems and interactions. These networks include protein-protein interaction networks, metabolic networks, gene regulatory networks, and more. Graph theory helps researchers understand the structure, function, and dynamics of these biological systems, and also, to uncover new relationships between genetic and metabolic entities.

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2 Network Models

Network models can be used to model complex networks, helping to explain their origins and evolution, as well as predicting their behavior and outcomes. Random graphs are graphs where nodes are connected randomly with some probability, and can serve as a baseline for comparison with real-world networks. Small-world networks are characterized by mostly local connections between nodes, but also some long-range connections that reduce the average distance between nodes, making them suitable for modeling social networks, neural networks, and power grids. Scale-free networks have a degree distribution that follows a power law, with a few nodes having many connections and many nodes having few connections. These models are suitable for modeling networks that grow through preferential attachment, such as the Internet, citation networks, and protein networks.

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Gareth Barkin

Dean of Operations at University of Puget Sound | Distinguished Professor of Anthropology and Asian Studies
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Network modeling can be really effective in anthropological research, especially for understanding the geographicly diffuse communities many of us now study. By mapping and analyzing social ties, movement patterns, and cultural exchanges, network models reveal the underlying structures and dynamics of group and intergroup interactions. Small-world models help elucidate tight-knit clusters within broader social fabrics, while scale-free networks highlight influential individuals or nodes, helping track how ideas and innovations spread. This quantitative approach can complement qualitative, ethnographic methods, providing more of a bird's eye understanding of community organization and information exchange.

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Nikolaos A. Papanikolaou

Associate Professor of Biological Chemistry, Aristotle University of Thessaloniki School of Medicine,Thessaloniki, Macedonia, Greece and Touro University, New York USA
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Networks play a vital role in understanding biological systems by representing and analyzing complex interactions and relationships between biological components, such as genes, proteins, and metabolites. Applications of biological networks range from identifying key players and pathways to uncovering disease mechanisms and aiding drug discovery. They provide a powerful framework for systems biology and interdisciplinary collaboration, advancing our knowledge of life sciences.

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3 Optimization Methods

Optimization methods can be used as a third way to model complex networks. These methods seek to find the best or optimal solution to a problem on a network, and can help design, improve, or control complex networks, as well as identify optimal strategies for decision making. Linear programming is an optimization method that optimizes a linear objective function subject to linear constraints. It can be used to model network flow optimization, shortest path routing, and network design. Integer programming is another optimization method that optimizes a linear or nonlinear objective function subject to linear or nonlinear constraints, with some variables being required to be integers. It can be used for network scheduling, network reliability, and network interdiction. Metaheuristics are stochastic or evolutionary techniques used to explore large and complex solution spaces and find near-optimal solutions. They can be used for network clustering, network alignment, and network inference.

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Nikolaos A. Papanikolaou

Associate Professor of Biological Chemistry, Aristotle University of Thessaloniki School of Medicine,Thessaloniki, Macedonia, Greece and Touro University, New York USA
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Optimization methods are a valuable approach for modeling complex networks, aiming to find optimal solutions and improve network design, control, and decision-making. Linear programming optimizes linear objectives with linear constraints, suitable for tasks like network flow, routing, and design. Integer programming extends to nonlinear objectives and constraints with integer variable requirements, useful for scheduling, reliability, and interdiction in networks. Metaheuristics, stochastic or evolutionary techniques, explore vast solution spaces to find near-optimal solutions, applied to tasks like clustering, alignment, and inference in complex networks.

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4 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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What are the most effective ways to model complex networks?

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1 Graph Theory

2 Network Models

3 Optimization Methods

4 Here’s what else to consider

Operations Research

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What are the most effective ways to model complex networks?

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1 Graph Theory

2 Network Models

3 Optimization Methods

4 Here’s what else to consider

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