Complex network in the context of "Structure"

A social network is a social structure consisting of a set of social actors (such as individuals or organizations), networks of dyadic ties, and other social interactions between actors. The social network perspective provides a set of methods for analyzing the structure of whole social entities along with a variety of theories explaining the patterns observed in these structures. The study of these structures uses social network analysis to identify local and global patterns, locate influential entities, and examine dynamics of networks. For instance, social network analysis has been used in studying the spread of misinformation on social media platforms or analyzing the influence of key figures in social networks.

Social networks and the analysis of them is an inherently interdisciplinary academic field which emerged from social psychology, sociology, statistics, and graph theory. Georg Simmel authored early structural theories in sociology emphasizing the dynamics of triads and "web of group affiliations". Jacob Moreno is credited with developing the first sociograms in the 1930s to study interpersonal relationships. These approaches were mathematically formalized in the 1950s and theories and methods of social networks became pervasive in the social and behavioral sciences by the 1980s. Social network analysis is now one of the major paradigms in contemporary sociology, and is also employed in a number of other social and formal sciences. Together with other complex networks, it forms part of the nascent field of network science.

Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive and semantic networks, and social networks, considering distinct elements or actors represented by nodes (or vertices) and the connections between the elements or actors as links (or edges). The field draws on theories and methods including graph theory from mathematics, statistical mechanics from physics, data mining and information visualization from computer science, inferential modeling from statistics, and social structure from sociology. The United States National Research Council defines network science as "the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena."

In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used to answer questions about the properties of typical graphs. Its practical applications are found in all areas in which complex networks need to be modeled – many random graph models are thus known, mirroring the diverse types of complex networks encountered in different areas. In a mathematical context, random graph refers almost exclusively to the Erdős–Rényi random graph model. In other contexts, any graph model may be referred to as a random graph.

The field of complex networks has emerged as an important area of science to generate novel insights into nature of complex systems The application of network theory to climate science is a young and emerging field. To identify and analyze patterns in global climate, scientists model climate data as complex networks.

Unlike most real-world networks where nodes and edges are well defined, in climate networks, nodes are identified as the sites in a spatial grid of the underlying global climate data set, which can be represented at various resolutions. Two nodes are connected by an edge depending on the degree of statistical similarity (that may be related to dependence) between the corresponding pairs of time-series taken from climate records.The climate network approach enables novel insights into the dynamics of the climate system over different spatial and temporal scales.

Systems biology is the computational and mathematical analysis and modeling of complex biological systems. It is a biology-based interdisciplinary field of study that focuses on complex interactions within biological systems, using a holistic approach (holism instead of the more traditional reductionism) to biological research. This multifaceted research domain necessitates the collaborative efforts of chemists, biologists, mathematicians, physicists, and engineers to decipher the biology of intricate living systems by merging various quantitative molecular measurements with carefully constructed mathematical models. It represents a comprehensive method for comprehending the complex relationships within biological systems. In contrast to conventional biological studies that typically center on isolated elements, systems biology seeks to combine different biological data to create models that illustrate and elucidate the dynamic interactions within a system. This methodology is essential for understanding the complex networks of genes, proteins, and metabolites that influence cellular activities and the traits of organisms.  One of the aims of systems biology is to model and discover emergent properties, of cells, tissues and organisms functioning as a system whose theoretical description is only possible using techniques of systems biology. By exploring how function emerges from dynamic interactions, systems biology bridges the gaps that exist between molecules and physiological processes.

As a paradigm, systems biology is usually defined in antithesis to the so-called reductionist paradigm (biological organisation), although it is consistent with the scientific method. The distinction between the two paradigms is referred to in these quotations: "the reductionist approach has successfully identified most of the components and many of the interactions but, unfortunately, offers no convincing concepts or methods to understand how system properties emerge ... the pluralism of causes and effects in biological networks is better addressed by observing, through quantitative measures, multiple components simultaneously and by rigorous data integration with mathematical models." (Sauer et al.) "Systems biology ... is about putting together rather than taking apart, integration rather than reduction. It requires that we develop ways of thinking about integration that are as rigorous as our reductionist programmes, but different. ... It means changing our philosophy, in the full sense of the term." (Denis Noble)