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In information theory, the graph entropy is a measure of the information rate achievable by communicating symbols over a channel in which certain pairs
Graph_entropy
Average uncertainty in variable's states
probabilities of the symbols. Entropy estimation Entropy power inequality Fisher information Graph entropy Hamming distance History of entropy History of information
Entropy_(information_theory)
Maximum-entropy random graph models are random graph models used to study complex networks subject to the principle of maximum entropy under a set of structural
Maximum-entropy random graph model
Maximum-entropy_random_graph_model
Measure of connection disorder in a network
network entropy is a disorder measure derived from information theory to describe the level of randomness and the amount of information encoded in a graph. It
Network_entropy
Topics referred to by the same term
measuring the exponential rate of volume growth of a Riemannian metric Graph entropy, a measure of the information rate achievable by communicating symbols
Entropy_(disambiguation)
Structural analysis of a network
undirected graphs and related entropies. Birkhäuser. p. 380. ISBN 978-0-8176-4903-6. Chung, Zhao, Fan, Wenbo (2010). "PageRank and Random Walks on Graphs". Fete
Biased_random_walk_on_a_graph
Graph relating temperature and entropy during a thermodynamic process or cycle
thermodynamics, a temperature–entropy (T–s) diagram is a thermodynamic diagram used to visualize changes to temperature (T ) and specific entropy (s) during a thermodynamic
Temperature–entropy_diagram
Measurement scale based on orders of magnitude
mean Log semiring Preferred number Semi-log plot Order of magnitude Entropy Entropy (information theory) pH Richter magnitude scale "Slide Rule Sense:
Logarithmic_scale
Measure of distance to normality
to normality. It is also known as negative entropy or syntropy. The concept and phrase "negative entropy" was introduced by Erwin Schrödinger in his
Negentropy
Type of biased random walk on a graph
A maximal entropy random walk (MERW) is a popular type of biased random walk on a graph, in which transition probabilities are chosen accordingly to the
Maximal_entropy_random_walk
Property of a thermodynamic system
Entropy is a thermodynamic state variable that quantifies the probabilistic distribution of accessible microstates in a system. The term and the concept
Entropy
Company database
Jitesh; Adibi, Jafar (2005). "Discovering important nodes through graph entropy the case of Enron email database". Proceedings of the 3rd international
Enron_Corpus
American computer scientist
is a new type of graph product, called the zig-zag product. Taking a product of a large graph with a small graph, the resulting graph inherits (roughly)
Salil_Vadhan
Entropy of a process with only two probable values
In information theory, the binary entropy function, denoted H ( p ) {\displaystyle \operatorname {H} (p)} or H b ( p ) {\displaystyle \operatorname
Binary_entropy_function
Approximate nearest neighbor search algorithm
datasets. HNSW stores vectors in a graph. Each vector is a node, and links connect it to some nearby vectors. The graph has several layers: upper layers
Hierarchical navigable small world
Hierarchical_navigable_small_world
Two closely related models for generating random graphs
the mathematical field of graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random
Erdős–Rényi_model
Procedures for constructing new graphs in graph theory
graph from an initial one by a complex change, such as: transpose graph; complement graph; line graph; graph minor; graph rewriting; power of graph;
Graph_operations
Graph generated by a random process
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability
Random_graph
Probability distribution that has the most entropy of a class
In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of
Maximum entropy probability distribution
Maximum_entropy_probability_distribution
Process forming a path from many random steps
walk – Model for a random simple path Maximal entropy random walk – Type of biased random walk on a graph Self-avoiding walk – Sequence of moves on a lattice
Random_walk
Type of thermodynamic potential
liquid, and part vapor, and by using a three-dimensional volume-entropy-internal energy graph, Gibbs was able to determine three states of equilibrium, i
Gibbs_free_energy
network theory, the Braunstein–Ghosh–Severini entropy (BGS entropy) of a network is the von Neumann entropy of a density matrix given by a normalized Laplacian
Braunstein–Ghosh–Severini entropy
Braunstein–Ghosh–Severini_entropy
In mathematics, the entropy influence conjecture is a statement about Boolean functions originally conjectured by Ehud Friedgut and Gil Kalai in 1996
Entropy_influence_conjecture
Network whose degree distribution follows a power law
transformation which converts random graphs to their edge-dual graphs (or line graphs) produces an ensemble of graphs with nearly the same degree distribution
Scale-free_network
Clustering and community detection algorithm
well-connected. Consider, for example, the following graph: Three communities are present in this graph (each color represents a community). Additionally
Leiden_algorithm
Idealized thermodynamic cycle
equal to zero (adiabatic process). A Carnot cycle plotted on a Temperature-entropy diagram (Figure 4) is rather simple. Isothermic paths are horizontal, adiabatic
Carnot_cycle
Sparse graph with strong connectivity
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander
Expander_graph
Measure used in digital signal processing to characterize an audio spectrum
Spectral flatness or tonality coefficient, also known as Wiener entropy, is a measure used in digital signal processing to characterize an audio spectrum
Spectral_flatness
classified by total entropy. The entropy content of graphs has been considered throughout fields of math and computer science. Design of entropy networks and
Entropy_network
Graph where most nodes are reachable in a small number of steps
network example Hubs are bigger than other nodes A small-world network is a graph characterized by a high clustering coefficient and low distances. In an
Small-world_network
algorithm for constructing maximum-cardinality matching on graphs. Coloring algorithm: algorithms for graph (vertex or edge) coloring (subject to constraints,
List_of_algorithms
Method of generating random small-world graphs
The Watts–Strogatz model is a random graph generation model that produces graphs with small-world properties, including short average path lengths and
Watts–Strogatz_model
Idea in quantum gravity
and Erik Verlinde explore links between gravity and entropy, Verlinde being known for an entropic gravity proposal. The Einstein equation for gravity
Induced_gravity
Methods of estimating differential entropy given some observations
2007.913132 Costa, J.A.; Hero, A.O. (2004), Geodesic entropic graphs for dimension and entropy estimation in manifold learning. In Signal Processing
Entropy_estimation
Random graph model in applied mathematics
random graph model subject to the principle of maximum entropy under constraints on the expectation of the degree sequence of sampled graphs. Whereas
Soft_configuration_model
Statistical models for network analysis
Exponential family random graph models (ERGMs) are a set of statistical models used to study the structure and patterns within networks, such as those
Exponential family random graph models
Exponential_family_random_graph_models
Knowledge base that represents semantic relations between concepts in a network
used as a form of knowledge representation. It is a directed or undirected graph consisting of vertices, which represent concepts, and edges, which represent
Semantic_network
Thermodynamic process in which temperature remains constant
equation is shown in the graph in Figure 1. Each curve is called an isotherm, meaning a curve at a same temperature T. Such graphs are termed indicator diagrams
Isothermal_process
Python library for graphs and networks
NetworkX is a Python library for studying graphs and networks. NetworkX is free software released under the BSD-new license. NetworkX began development
NetworkX
Degree of connectedness within a graph
In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position
Centrality
Hungarian mathematician (1941–2019)
289–297. Körner, J.; K. Marton (1988). "Random access communication and graph entropy". IEEE Transactions on Information Theory. 34 (2): 312–314. doi:10.1109/18
Katalin_Marton
Ionic structure in solution
called graphs, and their properties, such as graph spectrum, degree distribution, clustering coefficient, minimum path length, and graph entropy, are calculated
Ion_network
American computer scientist
and Parametric Network Entropies, PLoS ONE 6(1): 2011, e15733. Matthias Dehmer and Abbe Mowshowitz, A history of graph entropy measures, Information Sciences
Abbe_Mowshowitz
Relation between temperature and the equilibrium constant of a chemical reaction
_{r}S^{\ominus }}{R}}.} This graph is called the "Van 't Hoff plot" and is widely used to estimate the enthalpy and entropy of a chemical reaction. From
Van_'t_Hoff_equation
Network that allows computers to share resources and communicate with each other
(RGG) Hyperbolic (HGN) Hierarchical Stochastic block Blockmodeling Maximum entropy Soft configuration LFR Benchmark Dynamics Boolean network agent based Epidemic/SIR
Computer_network
Network with non-trivial topological features
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
Complex_network
Standard hostname for a networked device's loopback interface
(RGG) Hyperbolic (HGN) Hierarchical Stochastic block Blockmodeling Maximum entropy Soft configuration LFR Benchmark Dynamics Boolean network agent based Epidemic/SIR
Localhost
Process by which people befriend similar people
policies have a decreased influence on fertility rates in such populations. In graph representation learning, homophily means that nodes with the same label
Homophily
Analysis of social structures using network and graph theory
process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of nodes (individual
Social_network_analysis
Mathematical theory on behavior of connected clusters in a random graph
bottom? Similarly, one can ask, given a connected graph at what fraction 1 – p of failures the graph will become disconnected (no large component). The
Percolation_theory
Italian computer scientist
he introduced quantum graphity, a random graph model of spacetime. He also co-introduced the Braunstein–Ghosh–Severini entropy. Severini serves on the
Simone_Severini
Academic field
foundation of graph theory, a branch of mathematics that studies the properties of pairwise relations in a network structure. The field of graph theory continued
Network_science
A hyperbolic geometric graph (HGG) or hyperbolic geometric network (HGN) is a special type of spatial network where (1) latent coordinates of nodes are
Hyperbolic_geometric_graph
Machine learning algorithm
usual Boltzmann-Gibbs or Shannon entropy. In this sense, the Gini impurity is nothing but a variation of the usual entropy measure for decision trees. Used
Decision_tree_learning
Mixing property of Markov chains and graphs
In theoretical computer science, graph theory, and mathematics, the conductance is a parameter of a Markov chain that is closely tied to its mixing time
Conductance_(graph_theory)
Partitioning a digital image into segments
selected). Several popular methods are used in industry including the maximum entropy method, balanced histogram thresholding, Otsu's method (maximum variance)
Image_segmentation
Social structure made up of a set of social actors
field which emerged from social psychology, sociology, statistics, and graph theory. Georg Simmel authored early structural theories in sociology emphasizing
Social_network
Chart used to show conditions at which physical phases of a substance occur
properties may be graphed in phase diagrams. Examples of such thermodynamic properties include specific volume, specific enthalpy, or specific entropy. For example
Phase_diagram
In graph theory, the mathematically simplest spatial network
In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing
Random_geometric_graph
Study of graphs as a representation of relations between discrete objects
science, and network science, network theory is a part of graph theory. It defines networks as graphs where the vertices or edges possess attributes. Network
Network_theory
Binary operation in graph theory
preserving the expansion. Graph operations Reingold, O.; Vadhan, S.; Wigderson, A. (2000), "Entropy waves, the zig-zag graph product, and new constant-degree
Zig-zag_product
Method of representing systems
relations between various biological entities. In general, networks or graphs are used to capture relationships between entities or objects. A network
Biological_network
Theory of quantum gravity merging quantum mechanics and general relativity
hence, it has no entropy. It appears, then, that one can violate the second law of thermodynamics by dropping an object with nonzero entropy into a black
Loop_quantum_gravity
Concept in network science
stochastic block model is a generative model for random graphs. This model tends to produce graphs containing communities, subsets of nodes characterized
Stochastic_block_model
Graphical representation of energy flows in physical systems
A bond graph is a graphical representation of the energy flows though and between physical dynamical systems including those in the electrical, mechanical
Bond_graph
Network representing spatial objects
A spatial network (sometimes also geometric graph) is a graph in which the vertices or edges are spatial elements associated with geometric objects, i
Spatial_network
Set of random variables
of random variables having a Markov property described by an undirected graph. In other words, a random field is said to be a Markov random field if it
Markov_random_field
Arrangement of a communication network
network and may be depicted physically or logically. It is an application of graph theory wherein communicating devices are modeled as nodes and the connections
Network_topology
Network analysis and visualization package for Microsoft Excel
elements of a graph structure such as edges and nodes. NodeXL can also import a variety of graph formats such as edgelists, adjacency matrices, GraphML, UCINet
NodeXL
Archimedean solid with 8 faces
World Cup. In the mathematical field of graph theory, a truncated tetrahedral graph is an Archimedean graph, the graph of vertices and edges of the truncated
Truncated_tetrahedron
Heat required to raise the temperature of a given unit of mass of a substance
dimensionless entropy measured in bits. From the definition of entropy T d S = δ Q , {\displaystyle T\,{\text{d}}S=\delta Q,} the absolute entropy can be calculated
Specific_heat_capacity
Pair of values which express a thermodynamic system's internal energy
expressed in terms of pairs of conjugate variables such as temperature and entropy, pressure and volume, or chemical potential and particle number. In fact
Conjugate variables (thermodynamics)
Conjugate_variables_(thermodynamics)
Measure of network community structure
Modularity is a measure of the structure of networks or graphs which measures the strength of division of a network into modules (also called groups, clusters
Modularity_(networks)
Number of vertices with unambiguous distances
In graph theory, the metric dimension of a graph G is the minimum cardinality of a subset S of vertices such that all other vertices are uniquely determined
Metric dimension (graph theory)
Metric_dimension_(graph_theory)
Study of graphs defined by geometric means
Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter
Geometric_graph_theory
Sequence of data points over time
Correlation entropy Approximate entropy Sample entropy Fourier entropy [uk] Wavelet entropy Dispersion entropy Fluctuation dispersion entropy Rényi entropy Higher-order
Time_series
Negative of a convex function
and information theory, entropy is a concave function. In the case of thermodynamic entropy, without phase transition, entropy as a function of extensive
Concave_function
German scientific academic (1863-1935)
particularly for water, steam, and moist air. Mollier diagrams (enthalpy-entropy charts) are routinely used by engineers in the design work associated with
Richard_Mollier
Thermodynamic cycle that includes the basic Stirling engine
realistic representation of most real Stirling engines. The four points in the graph indicate the crank angle in degrees. The adiabatic Stirling cycle is similar
Stirling_cycle
Value used to initialize a pseudo-random number generator
pseudorandomly generated, having the seed will allow one to obtain the key. High entropy is important for selecting good random seed data. Random seeds need to
Random_seed
Disparity filter is a network reduction algorithm (a.k.a. graph sparsification algorithm ) to extract the backbone structure of undirected weighted network
Disparity filter algorithm of weighted network
Disparity_filter_algorithm_of_weighted_network
Clustering and community detection algorithm
function aggregateGraph returns a new graph whose vertices are the partition of the old graph, and whose edges are calculated using the old graph. This function
Louvain_method
Measure of centrality in a network based on nodal influence
In graph theory, the Katz centrality or alpha centrality of a node is a measure of centrality in a network. It was introduced by Leo Katz in 1953 and
Katz_centrality
2.71828…, base of natural logarithms
total entropy. Using the natural logarithm gives entropy units in nats (as opposed, for example, to the use of the base-2 logarithm giving entropy in bits)
E_(mathematical_constant)
Tendency for similar nodes to be connected
entropy state—which is usually disassortative. The table also has the value of r calculated analytically for two models of networks: the random graph
Assortativity
State function whose change relates to the system's maximal work output
liquid, and part vapor, and by using a three-dimensional volume-entropy-internal energy graph, Gibbs was able to determine three states of equilibrium, i
Thermodynamic_free_energy
Thermodynamic process in which no mass or heat is exchanged with surroundings
north-east (31° from V axisaxis). If adiabats and isotherms are graphed at regular intervals of entropy and temperature, respectively (like altitude on a contour
Adiabatic_process
Concept in graph theory
the cliques in the original graph while the edges of the clique graph record the overlap of the clique in the original graph. Applying any of the previous
Community_structure
Principles governing bonding in ice
directed-graph (arrows) and can be either ordered or disordered. In 1935, Linus Pauling used the ice rules to calculate the residual entropy (zero temperature
Ice_rules
In mathematics and theoretical computer science, entropy compression is an information theoretic method for proving that a random process terminates,
Entropy_compression
Notion in statistics
retinal photoreceptors. Fisher information is related to relative entropy. The relative entropy, or Kullback–Leibler divergence, between two distributions p
Fisher_information
Reversible transition in amorphous materials
crystalline. Glass is believed to exist in a kinetically locked state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass
Glass_transition
Conjecture in graph theory
Lee in 2013. Li and Szegedy's paper also used entropy methods to prove the property for a class of graphs called "reflection trees." Kim, Lee, and Lee's
Sidorenko's_conjecture
Concept in network science
In the study of graphs and networks, the degree of a node in a network is the number of connections it has to other nodes and the degree distribution is
Degree_distribution
Scale-free network generation algorithm
they have power-law (or scale-free) degree distributions, while random graph models such as the Erdős–Rényi (ER) model and the Watts–Strogatz (WS) model
Barabási–Albert_model
Family of random graph models
random graph models (ERGMs) and generates random graphs by constraining the expected degree sequence while maximizing the entropy of the graph model.
Configuration_model
Theorem in graph theory
In graph theory, the graph removal lemma states that when a graph contains few copies of a given subgraph, then all of the copies can be eliminated by
Graph_removal_lemma
Network for communications over distance
science Theory Graph Complex network Contagion Small-world Scale-free Community structure Percolation Evolution Controllability Graph drawing Social capital
Telecommunications_network
NP-hard problem in combinatorial optimization
version of the TSP (where given a length L, the task is to decide whether the graph has a tour whose length is at most L) belongs to the class of NP-complete
Travelling_salesman_problem
Analysing a string of symbols, according to the rules of a formal grammar
include straightforward PCFGs (probabilistic context-free grammars), maximum entropy, and neural nets. Most of the more successful systems use lexical statistics
Parsing
GRAPH ENTROPY
GRAPH ENTROPY
Boy/Male
Hindu, Indian
Efficient; Conqueror of Miseries; Bond in Affection; Capable; Mysterious; Different than Others; Smart; Most Mysterious Vastu Grah 'Rahu'; Son of Lord Buddha; Son of Goddess Durga; Truth Follower; Best of All
Biblical
a grape; a knot
Boy/Male
Indian
Grape
Boy/Male
Biblical
A grape, a knot.
Girl/Female
Hindu
Grape, Belonging to kashmir
Girl/Female
Tamil
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Grape, Belonging to kashmir
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Boy/Male
Hindu, Indian, Punjabi, Sikh
From Kashmir; Grape
Girl/Female
Indian
Grape like
Boy/Male
Muslim
Grape
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Female
Thai/Siamese
Thai name A-GUN means "grape."
Boy/Male
Biblical
A grape, a knot.
Girl/Female
Afghan, Arabic, Hebrew, Indian, Muslim, Parsi, Sanskrit
Grape Presser; World; Song; Universe
Girl/Female
Indian
Grape vine
Girl/Female
Muslim
Grape vine
Boy/Male
African, Arabic
Grape Vines
Girl/Female
Muslim
Grape like
Boy/Male
Afghan, Hebrew, Indian, Parsi, Sanskrit
Grape Presser; World; Song
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Boy/Male
Arabic, Modern
Grape
GRAPH ENTROPY
GRAPH ENTROPY
Boy/Male
Hindu, Indian, Marathi
Lord Shiva
Boy/Male
Assamese, Bengali, Hindu, Indian, Marathi, Sanskrit, Sindhi
Indestructible
Girl/Female
Greek American Scandinavian
Reaper.
Girl/Female
Arabic, Muslim
Victory of Allah
Girl/Female
Australian, Italian
Lady; From the Respectful Title Donna
Girl/Female
Muslim/Islamic
Unique The One
Male
Scottish
Scottish form of Greek Georgios, SEÃ’RAS means "earth-worker, farmer."
Boy/Male
Tamil
Young lady
Male
Russian
(Евгений) Variant spelling of Russian Evgeniy, YEVGENIY means "well born."Â
Girl/Female
American, Arabic, Chinese, Muslim
Most Beautiful One
GRAPH ENTROPY
GRAPH ENTROPY
GRAPH ENTROPY
GRAPH ENTROPY
GRAPH ENTROPY
a.
Composed of, or resembling, grapes.
n.
A sort of grape.
n.
Grapeshot.
n.
A well-known edible berry growing in pendent clusters or bunches on the grapevine. The berries are smooth-skinned, have a juicy pulp, and are cultivated in great quantities for table use and for making wine and raisins.
n.
See Grasshopper, and Frog hopper, Grape hopper, Leaf hopper, Tree hopper, under Frog, Grape, Leaf, and Tree.
n.
The Hartford grape, a variety of grape first raised at Hartford, Connecticut, from the Northern fox grape. Its large dark-colored berries ripen earlier than those of most other kinds.
n.
A plant of the genus Muscari; grape hyacinth.
n.
A grape of many varieties and colors.
n.
The cultivation of the vine; grape growing.
n.
A seed of the grape.
a.
Full of small kernels like a grape.
n.
A grape dried in the sun; a raisin.
n.
A grape, or a bunch of grapes.
n.
The plant which bears this fruit; the grapevine.
n.
A white grape, esteemed for the table.
n.
A mangy tumor on the leg of a horse.
n.
A variety of shaddock, called also grape fruit.
a.
Resembling a grape.