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Networks such as the previous one are commonly called feedforward, because their graph is a directed acyclic graph. Networks with cycles are commonly called recurrent . Such networks are commonly depicted in the manner shown at the top of the figure, where f {\displaystyle \textstyle f} is shown as dependent upon itself.
Stochastic block model – Concept in network science, a generalization of the Erdős–Rényi model for graphs with latent community structure; Watts–Strogatz model – Method of generating random small-world graphs; Barabási–Albert model – Scale-free network generation algorithm
Graph attention network is a combination of a graph neural network and an attention layer. The implementation of attention layer in graphical neural networks helps provide attention or focus to the important information from the data instead of focusing on the whole data. A multi-head GAT layer can be expressed as follows:
In the mathematical theory of artificial neural networks, universal approximation theorems are theorems [1] [2] of the following form: Given a family of neural networks, for each function from a certain function space, there exists a sequence of neural networks ,, … from the family, such that according to some criterion.
Example of a directed acyclic graph on four vertices. If the network structure of the model is a directed acyclic graph, the model represents a factorization of the joint probability of all random variables. More precisely, if the events are , …, then the joint probability satisfies
This data structure, which is conceptually akin to a prefix tree, stores sub-graphs according to their structures and finds occurrences of each of these sub-graphs in a larger graph. One of the noticeable aspects of this data structure is that coming to the network motif discovery, the sub-graphs in the main network are needed to be evaluated.
Network neuroscience is an approach to understanding the structure and function of the human brain through an approach of network science, through the paradigm of graph theory. [1] A network is a connection of many brain regions that interact with each other to give rise to a particular function. [2]
Exponential Random Graph Models (ERGMs) are a family of statistical models for analyzing data from social and other networks. [1] [2] Examples of networks examined using ERGM include knowledge networks, [3] organizational networks, [4] colleague networks, [5] social media networks, networks of scientific development, [6] and others.