In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research (since 2000) inspired largely by empirical findings of real-world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks. Most social, biological, and technological networks display substantial non-trivial topological features, with patterns of connection between their elements that are neither purely regular nor purely random. Such features include a heavy tail in the degree distribution, a high clustering coefficient, assortativity or disassortativity among vertices, community structure, and hierarchical structure. In the case of directed networks these features also include reciprocity, triad significance profile and other features. In contrast, many of the mathematical models of networks that have been studied in the past, such as lattices and random graphs, do not show these features. The most complex structures can be realized by networks with a medium number of interactions. This corresponds to the fact that the maximum information content (entropy) is obtained for medium probabilities. Two well-known and much studied classes of complex networks are scale-free networks and small-world networks, whose discovery and definition are canonical case-studies in the field. Both are characterized by specific structural features—power-law degree distributions for the former and short path lengths and high clustering for the latter. However, as the study of complex networks has continued to grow in importance and popularity, many other aspects of network structures have attracted attention as well. The field continues to develop at a brisk pace, and has brought together researchers from many areas including mathematics, physics, electric power systems, biology, climate, computer science, sociology, epidemiology, and others.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related courses (22)
MATH-448: Statistical analysis of network data
A first course in statistical network analysis and applications.
MSE-431: Physical chemistry of polymeric materials
The student has a basic understanding of the physical and physicochemical principles which result from the chainlike structure of synthetic macromolecules. The student can predict major characteristic
ChE-411: Principles and applications of systems biology
The course introduces and develops the key concepts from systems biology and systems engineering in the context of complex biological networks. The lectures elaborate on techniques and methods to mode
Show more
Related lectures (61)
Structured Synaptic Connectivity
Explores the structured synaptic connectivity between hippocampal regions using techniques like mGRASP and modeling.
Swiss Energy Sector Overview
Offers an overview of the Swiss energy sector, emphasizing key actors and the transition process.
Human Wellbeing: Energy, Needs, and Sustainability
Delves into the intricate balance between energy, human needs, and sustainability, emphasizing the importance of satisfying human needs within ecological constraints.
Show more
Related publications (344)
Related concepts (23)
Clustering coefficient
In graph theory, a clustering coefficient is a measure of the degree to which nodes in a graph tend to cluster together. Evidence suggests that in most real-world networks, and in particular social networks, nodes tend to create tightly knit groups characterised by a relatively high density of ties; this likelihood tends to be greater than the average probability of a tie randomly established between two nodes (Holland and Leinhardt, 1971; Watts and Strogatz, 1998). Two versions of this measure exist: the global and the local.
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.
Social network
A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets 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 as well as 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 network dynamics.
Show more
Related MOOCs (6)
Intro to Traffic Flow Modeling and Intelligent Transport Systems
Learn how to describe, model and control urban traffic congestion in simple ways and gain insight into advanced traffic management schemes that improve mobility in cities and highways.
Intro to Traffic Flow Modeling and Intelligent Transport Systems
Learn how to describe, model and control urban traffic congestion in simple ways and gain insight into advanced traffic management schemes that improve mobility in cities and highways.
Neuronal Dynamics - Computational Neuroscience of Single Neurons
The activity of neurons in the brain and the code used by these neurons is described by mathematical neuron models at different levels of detail.
Show more

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.