Section 14: Networks
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Tulip is an information visualization framework dedicated to the analysis and visualization of relational data. Tulip aims to provide the developer with a complete library, supporting the design of interactive information visualization applications for relational data that can be tailored to the problems he or she is addressing. Written in C++ the framework enables the development of algorithms, visual encodings, interaction techniques, data models, and domain-specific visualizations. One of the goal of Tulip is to facilitates the reuse of components and allows the developers to focus on programming their application.
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In the study of complex networks , a network is said to have community structure if the nodes of the network can be easily grouped into (potentially overlapping) sets of nodes such that each set of nodes is densely connected internally. In the particular case of non-overlapping community finding, this implies that the network divides naturally into groups of nodes with dense connections internally and sparser connections between groups. But overlapping communities are also allowed. The more general definition is based on the principle that pairs of nodes are more likely to be connected if they are both members of the same community(ies), and less likely to be connected if they do not share communities. [ edit ] Properties
Complex systems present problems in mathematical modelling . Complex systems is a new approach to science that studies how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment. The equations from which complex system models are developed generally derive from statistical physics , information theory and non-linear dynamics , and represent organized but unpredictable behaviors of systems of nature that are considered fundamentally complex . The physical manifestations of such systems cannot be defined, so the usual choice is to refer to "the system" as the mathematical information model, without referring to the undefined physical subject the model represents.
Network theory is an area of computer science and network science and part of graph theory . It has application in many disciplines including statistical physics, particle physics , computer science, biology , economics , operations research , and sociology . Network theory concerns itself with the study of graphs as a representation of either symmetric relations or, more generally, of asymmetric relations between discrete objects. Applications of network theory include logistical networks, the World Wide Web , Internet, gene regulatory networks , metabolic networks, social networks , epistemological networks, etc.
Network science is an interdisciplinary academic field which studies complex networks such as telecommunication networks , computer networks , biological networks , cognitive and semantic networks , and social networks . 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." [ 1 ] [ edit ] Background and history The study of networks has emerged in diverse disciplines as a means of analyzing complex relational data. The earliest known paper in this field is the famous Seven Bridges of Königsberg written by Leonhard Euler in 1736.
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 real graphs. The study of complex networks is a young and active area of scientific research inspired largely by the empirical study of real-world networks such as computer networks and social networks . [ edit ] Definition 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 graph theory , a clustering coefficient is a measure of 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; [ 1 ] Watts and Strogatz, 1998 [ 2 ] ). Two versions of this measure exist: the global and the local. The global version was designed to give an overall indication of the clustering in the network, whereas the local gives an indication of the embeddedness of single nodes.
Steven H. Strogatz Networks are on our minds nowadays. Sometimes we fear their power — and with good reason. On 10 August 1996, a fault in two power lines in Oregon led, through a cascading series of failures, to blackouts in 11 US states and two Canadian provinces, leaving about 7 million customers without power for up to 16 hours 1 . The Love Bug worm, the worst computer attack to date, spread over the Internet on 4 May 2000 and inflicted billions of dollars of damage worldwide.
In the fields of computational linguistics and probability , an n -gram is a contiguous sequence of n items from a given sequence of text or speech. An n -gram could be any combination of letters. However, the items in question can be phonemes , syllables, letters, words or base pairs according to the application.