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5.0

Jun 30, 2018
06/18

by
Alfonso Allen-Perkins; Juan Manuel Pastor; Ernesto Estrada

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Degree ssortativity is the tendency for nodes of high degree (resp.low degree) in a graph to be connected to high degree nodes (resp. to low degree ones). It is sually quantified by the Pearson correlation coefficient of the degree-degree correlation. Here we extend this concept to account for the effect of second neighbours to a given node in a graph. That is, we consider the two-walks degree of a node as the sum of all the degrees of its adjacent nodes. The two-walks degree assortativity of a...

Topics: Physics, Computing Research Repository, Physics and Society, Social and Information Networks

Source: http://arxiv.org/abs/1704.03943

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9.0

Jun 29, 2018
06/18

by
Ernesto Estrada; Alhanouf Ali Alhomaidhi; Fawzi Al-Thukair

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We study a Gaussian matrix function of the adjacency matrix of artificial and real-world networks. In particular, we study the Gaussian Estrada index---an index characterizing the importance of eigenvalues close to zero. This index accounts for the information contained in the eigenvalues close to zero in the spectra of networks. Here we obtain bounds for this index in simple graphs, proving that it reaches its maximum for star graphs followed by complete bipartite graphs. We also obtain...

Topics: Physics and Society, Spectral Theory, Physics, Mathematics, Computing Research Repository, Social...

Source: http://arxiv.org/abs/1607.08812

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22

Jun 28, 2018
06/18

by
Ernesto Estrada; Eusebio Vargas-Estrada; Hiroyasu Ando

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We consider the question of determining how the topological structure influences a consensus dynamical process taking place on a network. By considering a large dataset of real-world networks we first determine that the removal of edges according to their communicability angle -an angle between position vectors of the nodes in an Euclidean communicability space- increases the average time of consensus by a factor of 5.68 in real-world networks. The edge betweenness centrality also identifies...

Topics: Social and Information Networks, Physics and Society, Computing Research Repository, Physics

Source: http://arxiv.org/abs/1507.05881

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7.0

Jun 30, 2018
06/18

by
Ernesto Estrada; Francesca Arrigo

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We propose a communication-driven mechanism for predicting triadic closure in complex networks. It is mathematically formulated on the basis of communicability distance functions that account for the quality of communication between nodes in the network. We study $25$ real-world networks and show that the proposed method predicts correctly $20\%$ of triadic closures in these networks, in contrast to the $7.6\%$ predicted by a random mechanism. We also show that the communication-driven method...

Topics: Physics, Computing Research Repository, Physics and Society, Social and Information Networks

Source: http://arxiv.org/abs/1411.5599

5
5.0

Jun 29, 2018
06/18

by
Ernesto Estrada; Grant Silver

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We introduce a new matrix function for studying graphs and real-world networks based on a double-factorial penalization of walks between nodes in a graph. This new matrix function is based on the matrix error function. We find a very good approximation of this function using a matrix hyperbolic tangent function. We derive a communicability function, a subgraph centrality and a double-factorial Estrada index based on this new matrix function. We obtain upper and lower bounds for the...

Topics: Physics and Society, Physics, Mathematics, Combinatorics, Computing Research Repository, Social and...

Source: http://arxiv.org/abs/1607.06807

5
5.0

Jun 29, 2018
06/18

by
Ernesto Estrada; Jean-Charles Delvenne; Naomichi Hatano; José L. Mateos; Ralf Metzler; Alejandro P. Riascos; Michael T. Schaub

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We develop a model for a random walker with long-range hops on general graphs. This random multi-hopper jumps from a node to any other node in the graph with a probability that decays as a function of the shortest-path distance between the two nodes. We consider here two decaying functions in the form of the Laplace and Mellin transforms of the shortest-path distances. Remarkably, when the parameters of these transforms approach zero asymptotically, the multi-hopper's hitting times between any...

Topics: Physics and Society, Statistical Mechanics, Condensed Matter, Physics, Mathematics, Probability,...

Source: http://arxiv.org/abs/1612.08631

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20

Jun 26, 2018
06/18

by
Ernesto Estrada; Matthew Sheerin

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A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the random rectangular graphs (RRGs) generated by this model are then studied as a function of the rectangle sides lengths a and b=1/a, and the radius r used to connect the nodes. When a=1 we recover the RGG, and when a-->infinity the very elongated rectangle...

Topics: Mathematics, Physics, Mathematical Physics, Physics and Society

Source: http://arxiv.org/abs/1502.02577

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28

Jun 28, 2018
06/18

by
Ernesto Estrada; Michele Benzi

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Core-satellite graphs (sometimes referred to as generalized friendship graphs) are an interesting class of graphs that generalize many well known types of graphs. In this paper we show that two popular clustering measures, the average Watts-Strogatz clustering coefficient and the transitivity index, diverge when the graph size increases. We also show that these graphs are disassortative. In addition, we completely describe the spectrum of the adjacency and Laplacian matrices associated with...

Topics: Mathematics, Physics and Society, Combinatorics, Physics, Social and Information Networks,...

Source: http://arxiv.org/abs/1510.07954

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4.0

Jun 30, 2018
06/18

by
Ernesto Estrada; Naomichi Hatano

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We introduce the concept of communicability angle between a pair of nodes in a graph. We provide strong analytical and empirical evidence that the average communicability angle for a given network accounts for its spatial efficiency on the basis of the communications among the nodes in a network. We determine characteristics of the spatial efficiency of more than a hundred real-world complex networks that represent complex systems arising in a diverse set of scenarios. In particular, we find...

Topics: Physics, Mathematics, Physics and Society, Combinatorics

Source: http://arxiv.org/abs/1412.7388

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Jun 28, 2018
06/18

by
Ernesto Estrada; Sandro Meloni; Matthew Sheerin; Yamir Moreno

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The use of network theory to model disease propagation on populations introduces important elements of reality to the classical epidemiological models. The use of random geometric graphs (RGG) is one of such network models that allows for the consideration of spatial properties on disease propagation. In certain real-world scenarios -like in the analysis of a disease propagating through plants- the shape of the plots and fields where the host of the disease is located may play a fundamental...

Topics: Physics and Society, Mathematical Physics, Mathematics, Physics

Source: http://arxiv.org/abs/1507.06002