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A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P(k) of nodes in the network having k connections to other nodes goes for large values of k as
Scientometrics is a subfield of informetrics that studies quantitative aspects of scholarly literature. Major research issues include the measurement of the impact of research papers and academic journals, the understanding of scientific citations, and the use of such measurements in policy and management contexts. In practice there is a significant overlap between scientometrics and other scientific fields such as information systems, information science, science of science policy, sociology of science, and metascience. Critics have argued that overreliance on scientometrics has created a system of perverse incentives, producing a publish or perish environment that leads to low-quality research.
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 inspired largely by empirical findings of real-world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks.
Informetrics is the study of quantitative aspects of information, it is an extension and evolution of traditional bibliometrics and scientometrics. Informetrics uses bibliometrics and scientometrics methods to study mainly the problems of literature information management and evaluation of science and technology. Informetrics is an independent discipline that uses quantitative methods from mathematics and statistics to study the process, phenomena, and law of informetrics. Informetrics has gained more attention as it is a common scientific method for academic evaluation, research hotspots in discipline, and trend analysis.
The h-index is an author-level metric that measures both the productivity and citation impact of the publications, initially used for an individual scientist or scholar. The h-index correlates with success indicators such as winning the Nobel Prize, being accepted for research fellowships and holding positions at top universities. The index is based on the set of the scientist's most cited papers and the number of citations that they have received in other publications. The index has more recently been applied to the productivity and impact of a scholarly journal as well as a group of scientists, such as a department or university or country. The index was suggested in 2005 by Jorge E. Hirsch, a physicist at UC San Diego, as a tool for determining theoretical physicists' relative quality and is sometimes called the Hirsch index or Hirsch number.
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 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. A related but different problem is community search, where the goal is to find a community that a certain vertex belongs to.
Journal ranking is widely used in academic circles in the evaluation of an academic journal's impact and quality. Journal rankings are intended to reflect the place of a journal within its field, the relative difficulty of being published in that journal, and the prestige associated with it. They have been introduced as official research evaluation tools in several countries.
In the mathematical field of graph theory, the Erdős–Rényi model refers to one of two closely related models for generating random graphs or the evolution of a random network. These models are named after Hungarian mathematicians Paul Erdős and Alfréd Rényi, who introduced one of the models in 1959. Edgar Gilbert introduced the other model contemporaneously with and independently of Erdős and Rényi. In the model of Erdős and Rényi, all graphs on a fixed vertex set with a fixed number of edges are equally likely. In the model introduced by Gilbert, also called the Erdős–Rényi–Gilbert model, each edge has a fixed probability of being present or absent, independently of the other edges. These models can be used in the probabilistic method to prove the existence of graphs satisfying various properties, or to provide a rigorous definition of what it means for a property to hold for almost all graphs.
Mark Newman is a British physicist and Anatol Rapoport Distinguished University Professor of Physics at the University of Michigan, as well as an external faculty member of the Santa Fe Institute. He is known for his fundamental contributions to the fields of complex systems and complex networks, for which he was awarded the Lagrange Prize in 2014 and the APS Kadanoff Prize in 2024.
Modularity is a measure of the structure of networks or graphs which measures the strength of division of a network into modules. Networks with high modularity have dense connections between the nodes within modules but sparse connections between nodes in different modules. Modularity is often used in optimization methods for detecting community structure in networks. Biological networks, including animal brains, exhibit a high degree of modularity. However, modularity maximization is not statistically consistent, and finds communities in its own null model, i.e. fully random graphs, and therefore it cannot be used to find statistically significant community structures in empirical networks. Furthermore, it has been shown that modularity suffers a resolution limit and, therefore, it is unable to detect small communities.
The webgraph describes the directed links between pages of the World Wide Web. A graph, in general, consists of several vertices, some pairs connected by edges. In a directed graph, edges are directed lines or arcs. The webgraph is a directed graph, whose vertices correspond to the pages of the WWW, and a directed edge connects page X to page Y if there exists a hyperlink on page X, referring to page Y.
Cristopher David Moore, known as Cris Moore, is an American computer scientist, mathematician, and physicist. He is resident faculty at the Santa Fe Institute, and was formerly a full professor at the University of New Mexico. He is an elected Fellow of the American Physical Society, the American Mathematical Society, and the American Association for the Advancement of Science.
Filippo Menczer is an American and Italian academic. He is a University Distinguished Professor and the Luddy Professor of Informatics and Computer Science at the Luddy School of Informatics, Computing, and Engineering, Indiana University. Menczer is the Director of the Observatory on Social Media, a research center where data scientists and journalists study the role of media and technology in society and build tools to analyze and counter disinformation and manipulation on social media. Menczer holds courtesy appointments in Cognitive Science and Physics, is a founding member and advisory council member of the IU Network Science Institute, a former director the Center for Complex Networks and Systems Research, a senior research fellow of the Kinsey Institute, a fellow of the Center for Computer-Mediated Communication, and a former fellow of the Institute for Scientific Interchange in Turin, Italy. In 2020 he was named a Fellow of the ACM.
Scientific collaboration network is a social network where nodes are scientists and links are co-authorships as the latter is one of the most well documented forms of scientific collaboration. It is an undirected, scale-free network where the degree distribution follows a power law with an exponential cutoff – most authors are sparsely connected while a few authors are intensively connected. The network has an assortative nature – hubs tend to link to other hubs and low-degree nodes tend to link to low-degree nodes. Assortativity is not structural, meaning that it is not a consequence of the degree distribution, but it is generated by some process that governs the network’s evolution.
The Louvain method for community detection is a method to extract non-overlapping communities from large networks created by Blondel et al. from the University of Louvain. The method is a greedy optimization method that appears to run in time where is the number of nodes in the network.
The initial attractiveness is a possible extension of the Barabási–Albert model. The Barabási–Albert model generates scale-free networks where the degree distribution can be described by a pure power law. However, the degree distribution of most real life networks cannot be described by a power law solely. The most common discrepancies regarding the degree distribution found in real networks are the high degree cut-off and the low degree saturation. The inclusion of initial attractiveness in the Barabási–Albert model addresses the low-degree saturation phenomenon.
Zachary's karate club is a social network of a university karate club, described in the paper "An Information Flow Model for Conflict and Fission in Small Groups" by Wayne W. Zachary. The network became a popular example of community structure in networks after its use by Michelle Girvan and Mark Newman in 2002.
Author-level metrics are citation metrics that measure the bibliometric impact of individual authors, researchers, academics, and scholars. Many metrics have been developed that take into account varying numbers of factors.
The stochastic block model is a generative model for random graphs. This model tends to produce graphs containing communities, subsets of nodes characterized by being connected with one another with particular edge densities. For example, edges may be more common within communities than between communities. Its mathematical formulation was first introduced in 1983 in the field of social network analysis by Paul W. Holland et al. The stochastic block model is important in statistics, machine learning, and network science, where it serves as a useful benchmark for the task of recovering community structure in graph data.
The International School and Conference on Network Science, also called NetSci, is an annual conference focusing on networks. It is organized yearly since 2006 by the Network Science Society. Physicists are especially prominently represented among the participants, though people from other backgrounds attend as well. The study of networks expanded at the end of the twentieth century, with increasing citation of some seminal papers.
References
- ↑ Curriculum vitae, retrieved 2024-06-04.
- ↑ Aaron Clauset at the Mathematics Genealogy Project
- 1 2 Cummings, Dominic (2 January 2020). "'Two hands are a lot' — we're hiring data scientists, project managers, policy experts, assorted weirdos…". Dominic Cummings's Blog. Retrieved 4 January 2021.
- 1 2 Gibney, Elizabeth (7 January 2020). "Government call for science 'weirdos' prompts caution from researchers". Nature. doi:10.1038/d41586-020-00012-9.
- 1 2 Vaughan, Adam (7 January 2020). "Dominic Cummings wants 'weirdos' to help run the UK. Will it work?". New Scientist. Retrieved 4 January 2021.
- ↑ "Erdős–Rényi prize for young scientists". Network Science Society. Retrieved 4 June 2016.
- ↑ "ISSI Paper of the Year Award 2021" (PDF). International Society for Scientometrics and Informetrics. Retrieved 4 June 2021.
- ↑ "realitytvworld".
