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NetworkX
NetworkX is a Python (programming language), Python library for studying Graph (discrete mathematics), graphs and Network theory, networks. NetworkX is free software released under the BSD-new, BSD-new license. History NetworkX began development in 2002 by Aric A. Hagberg, Daniel A. Schult, and Pieter J. Swart.Aric A. Hagberg, Daniel A. Schult, Pieter J. SwartExploring Network Structure, Dynamics, and Function using NetworkX ''Proceedings of the 7th Python in Science conference (SciPy 2008)'', G. Varoquaux, T. Vaught, J. Millman (Eds.), pp. 11–15. It is supported by the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory. The package was crafted with the aim of creating tools to analyze data and intervention strategies for controlling the epidemic spread of disease, while also exploring the structure and dynamics of more general social, biological, and infrastructural systems. Inspired by Guido van Rossum's 1998 essay ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aric Hagberg
Aric Hagberg is an American applied mathematician and academic, working in nonlinear dynamics, pattern formation and complex systems. He is the division leader of the computer, computational, and statistical sciences division at Los Alamos National Laboratory. He was educated at the University of Arizona (PhD, 1994). Aric is also one of the authors of the NetworkX package.Aric A. Hagberg, Daniel A. Schult, Pieter J. SwartExploring Network Structure, Dynamics, and Function using NetworkX ''Proceedings of the 7th Python in Science conference (SciPy 2008)'', G. Varoquaux, T. Vaught, J. Millman (Eds.), pp. 11–15. References External links Hagberg's Google Scholar ProfileHagberg's Page at LANL's Center for Nonlinear Studies {{DEFAULTSORT:Hagberg, Aric Living people University of Arizona alumni Los Alamos National Laboratory personnel Year of birth missing (living people) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimum Spanning Trees
A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. That is, it is a spanning tree whose sum of edge weights is as small as possible. More generally, any edge-weighted undirected graph (not necessarily connected) has a minimum spanning forest, which is a union of the minimum spanning trees for its connected components. There are many use cases for minimum spanning trees. One example is a telecommunications company trying to lay cable in a new neighborhood. If it is constrained to bury the cable only along certain paths (e.g. roads), then there would be a graph containing the points (e.g. houses) connected by those paths. Some of the paths might be more expensive, because they are longer, or require the cable to be buried deeper; these paths would be represented by edges with larger weights ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SageMath
SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, group theory, differentiable manifolds, numerical analysis, number theory, calculus, and statistics. The first version of SageMath was released on 24 February 2005 as free and open-source software under the terms of the GNU General Public License version 2, with the initial goals of creating an "open source alternative to Magma, Maple, Mathematica, and MATLAB". The originator and leader of the SageMath project, William Stein, was a mathematician at the University of Washington. SageMath uses a syntax resembling Python's, supporting procedural, functional, and object-oriented constructs. Development Stein realized when designing Sage that there were many open-source mathematics software packages already written in different languages, namely C, C++, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dijkstra's Algorithm
Dijkstra's algorithm ( ) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. Dijkstra's algorithm finds the shortest path from a given source node to every other node. It can be used to find the shortest path to a specific destination node, by terminating the algorithm after determining the shortest path to the destination node. For example, if the nodes of the graph represent cities, and the costs of edges represent the distances between pairs of cities connected by a direct road, then Dijkstra's algorithm can be used to find the shortest route between one city and all other cities. A common application of shortest path algorithms is network routing protocols, most notably IS-IS (Intermediate System to Intermediate System) and OSPF (Open Shortest Path First). It is also employed as a subroutine in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clique (graph Theory)
In graph theory, a clique ( or ) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent. That is, a clique of a graph G is an induced subgraph of G that is complete. Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs. Cliques have also been studied in computer science: the task of finding whether there is a clique of a given size in a graph (the clique problem) is NP-complete, but despite this hardness result, many algorithms for finding cliques have been studied. Although the study of complete subgraphs goes back at least to the graph-theoretic reformulation of Ramsey theory by , the term ''clique'' comes from , who used complete subgraphs in social networks to model cliques of people; that is, groups of people all of whom know each other. Cliques have many other applications in the sciences and particularly in bioinformatics. Definiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glossary Of Graph Theory
This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by lines or edges. Symbols A B C D E F G H I J K L M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Graph
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''. Models A random graph is obtained by starting with a set of ''n'' isolated vertices and adding successive edges between them at random. The a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class (computer Programming)
In object-oriented programming, a class defines the shared aspects of objects created from the class. The capabilities of a class differ between programming languages, but generally the shared aspects consist of state ( variables) and behavior ( methods) that are each either associated with a particular object or with all objects of that class. Object state can differ between each instance of the class whereas the class state is shared by all of them. The object methods include access to the object state (via an implicit or explicit parameter that references the object) whereas class methods do not. If the language supports inheritance, a class can be defined based on another class with all of its state and behavior plus additional state and behavior that further specializes the class. The specialized class is a ''sub-class'', and the class it is based on is its ''superclass''. Attributes Object lifecycle As an instance of a class, an object is constructed from a class via '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GraphBLAS
GraphBLAS () is an API specification that defines standard building blocks for graph algorithms in the language of linear algebra. GraphBLAS is built upon the notion that a sparse matrix can be used to represent graphs as either an adjacency matrix or an incidence matrix. The GraphBLAS specification describes how graph operations (e.g. traversing and transforming graphs) can be efficiently implemented via linear algebraic methods (e.g. matrix multiplication) over different semirings. The development of GraphBLAS and its various implementations is an ongoing community effort, including representatives from industry, academia, and government research labs. Background Graph algorithms have long taken advantage of the idea that a graph can be represented as a matrix, and graph operations can be performed as linear transformations and other linear algebraic operations on sparse matrices. For example, matrix-vector multiplication can be used to perform a step in a breadth-first se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software Documentation
Software documentation is written text or illustration that accompanies computer software or is embedded in the source code. The documentation either explains how the software operates or how to use it, and may mean different things to people in different roles. Documentation is an important part of software engineering. Types of documentation include: * Requirements – Statements that identify attributes, capabilities, characteristics, or qualities of a system. This is the foundation for what will be or has been implemented. * Architecture/Design – Overview of software. Includes relations to an environment and construction principles to be used in design of software components. * Technical – Documentation of code, algorithms, interfaces, and APIs. * End user – Manuals for the end-user, system administrators and support staff. * Marketing – How to market the product and analysis of the market demand. Types Requirements documentation Requirements documentation is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kruskal’s Algorithm
Kruskal's algorithm finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected, it finds a minimum spanning tree. It is a greedy algorithm that in each step adds to the forest the lowest-weight edge that will not form a cycle. The key steps of the algorithm are sorting and the use of a disjoint-set data structure to detect cycles. Its running time is dominated by the time to sort all of the graph edges by their weight. A minimum spanning tree of a connected weighted graph is a connected subgraph, without cycles, for which the sum of the weights of all the edges in the subgraph is minimal. For a disconnected graph, a minimum spanning forest is composed of a minimum spanning tree for each connected component. This algorithm was first published by Joseph Kruskal in 1956, and was rediscovered soon afterward by . Other algorithms for this problem include Prim's algorithm, Borůvka's algorithm, and the reverse-delete algorithm. Algorithm The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
