Conclusion first: state space is actually a graph structure. The nodes in the graph represent the states, and the edges in the graph represent the connections before the states. This connection is the various relations given in the title. ...
To encapsulate as much information as possible within the molecular graph, we include a plethora of atomic features: atom type, number of heavy atom neighbours, formal charge, hybridisation type, whether the atom is in a ring, whether the atom is aromatic, atomic mass, Van der Waals radiu...
To extend the above approaches (i) and (ii) to complex and analytically intractable systems, different methods relying on artificial neural networks (ANNs) have been used to represent certain functions that appear in the formulation of optimal control problems. One possibility is to use ANNs to ...
Using a polynomial time algorithm, we comment on computer experiments with which we can distinguish cospectral (non-isomorphic) graphs. Keywords: graph isomorphism problem; cospectral graphs; generalized adjacency matrix MSC: 05C60; 68R05 Citation: Wananiyakul, S.; Steuding, J.; Tongsomporn, J...
To represent the graph, we use an adjacency matrix. An adjacency matrix consists of a two-dimensional grid. Each row or column in the grid represents a node. For an unweighted graph, as shown above, if the value at the position(i,j)is 1 in the grid, it means that nodeiand nodejare...
A distributed system is also beneficial as graph analytics is often computation intensive. Using the memory and the computation power of all the machines, we may be able to operate on graphs of any size. ab cd ef i gh k (a) A graph j l a, d c, f b, j e, g h, i k, l (...
Whereas most measure formulas use sums and products over nodes and edges, some of them need search algorithms on graph data structures to find, e.g. shortest path lengths between node pairs. Technically seen, there are different classical data structures which represent graphs (see Fig. 1). ...
and a the numerical value of an indicator can represent at most one of the semantic dimensions of a polysemous construct, ergo, ideally IDR should be measured through a coordinated system of indicators not with a single measure (Rafols,2019; Marres & de Rijcke,2020; Stirling,2023). ...
(where the length of the edges between the nodes represent how strongly they are related), and the only degree of freedom the algorithm has is the rotation of the graph. But especially in graphs with many nodes, the placement tells us only a very rough story, and should not be over-...
Values close to 1 detect what we called here “authority”. Operationally, given a graph G=(N,V) with N nodes and V links, if A is its adjacency matrix, the hub index is computed as the eigenvector of the matrix AAT, while the authority index is computed as the eigenvector of the...