arXiv subjects

Ernesto Estrada

Publications and source records attributed to Ernesto Estrada.

At least 55 records · Page 3Linked to original sources

arXiv2015

Communicability Angle and the Spatial Efficiency of Networks

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 that the communicability angle correlates very well with the experimentally measured value of the relative packing efficiency of proteins that are represented as residue networks. We finally show how we can modulate the spatial efficiency of a network by tuning the weights of the edges of the networks. This allows us to predict effects of external stresses on the spatial efficiency of a network as well as to design strategies to improve important parameters in real-world complex systems.

physics.soc-ph↗

arXiv2015

Communicability Angles Reveal Critical Edges for Network Consensus Dynamics

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 -in a smaller proportion- those critical edges for the consensus dynamics, i.e., its removal increases the time of consensus by a factor of 3.70. We justify theoretically these findings on the basis of the role played by the algebraic connectivity and the isoperimetric number of networks on the dynamical process studied, and their connections with the properties mentioned before. Finally, we study the role played by global topological parameters of networks on the consensus dynamics. We determine that the network density and the average distance-sum -an analogous of the node degree for shortest-path distances, account for more than 80% of the variance of the average time of consensus in the real-world networks studied.

physics.soc-ph↗

arXiv2015

Predicting triadic closure in networks using communicability distance functions

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 outperforms the random mechanism in explaining the clustering coefficient, average path length, and average communicability. The new method also displays some interesting features with regards to optimizing communication in networks.

cs.SI↗

arXiv2015

Random Rectangular Graphs

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 generated resembles a one-dimensional RGG. We obtain here analytical expressions for the average degree, degree distribution, connectivity, average path length and clustering coefficient for RRG. These results provide evidence that show that most of these properties depend on the connection radius and the side length of the rectangle, usually in a monotonic way. The clustering coefficient, however, increases when the square is transformed into a slightly elongated rectangle, and after this maximum it decays with the increase of the elongation of the rectangle. We support all our findings by computational simulations that show the goodness of the theoretical models proposed for RRGs.

physics.soc-ph↗

arXiv2014

Are Social Networks Really Balanced?

There is a long-standing belief that in social networks with simultaneous friendly/hostile interactions (signed networks) there is a general tendency to a global balance. Balance represents a state of the network with lack of contentious situations. Here we introduce a method to quantify the degree of balance of any signed (social) network. It accounts for the contribution of all signed cycles in the network and gives, in agreement with empirical evidences, more weight to the shorter than to the longer cycles. We found that, contrary to what is believed, many signed social networks -- in particular very large directed online social networks -- are in general very poorly balanced. We also show that unbalanced states can be changed by tuning the weights of the social interactions among the agents in the network.

physics.soc-ph↗

arXiv2013

Communicability reveals a transition to coordinated behavior in multiplex networks

We analyse the flow of information in multiplex networks by means of the communicability function. First, we generalize this measure from its definition from simple graphs to multiplex networks. Then, we study its relevance for the analysis of real-world systems by studying a social multiplex where information flows using formal/informal channels and an air transportation system where the layers represent different air companies. Accordingly, the communicability, which is essential for the good performance of these complex systems, emerges at a systemic operation point in the multiplex where the performance of the layers operates in a coordinated way very differently from the state represented by a collection of unconnected networks.

physics.soc-ph↗

arXiv2013

Peer Pressure Shapes Consensus, Leadership, and Innovations in Social Groups

What is the effect of the combined direct and indirect social influences-peer pressure (PP)-on a social groups collective decisions? We present a model that captures PP as a function of the socio-cultural distance between individuals in a social group. Using this model and empirical data from 15 real-world social networks we found that the PP level determines how fast a social group reaches consensus. More importantly, the levels of PP determine the leaders who can achieve full control of their social groups. PP can overcome barriers imposed upon a consensus by the existence of tightly connected communities with local leaders or the existence of leaders with poor cohesiveness of opinions. A moderate level of PP is also necessary to explain the rate at which innovations diffuse through a variety of social groups.

physics.soc-ph↗

arXiv2013

Walk Entropies in Graphs

Entropies based on walks on graphs and on their line-graphs are defined. They are based on the summation over diagonal and off-diagonal elements of the thermal Green's function of a graph also known as the communicability. The walk entropies are strongly related to the walk regularity of graphs and line-graphs. They are not biased by the graph size and have significantly better correlation with the inverse participation ratio of the eigenmodes of the adjacency matrix than other graph entropies. The temperature dependence of the walk entropies is also discussed. In particular, the walk entropy of graphs is shown to be non-monotonic for regular but non-walk-regular graphs in contrast to non-regular graphs.

math-ph↗

arXiv2013

Graph and Network Theory in Physics

A book Chapter consisting of some of the main areas of research in graph theory applied to physics. It includes graphs in condensed matter theory, such as the tight-binding and the Hubbard model. It follows the study of graph theory and statistical physics by means of the analysis of the Potts model. Then, we consider the use of graph polynomials in solving Feynman integrals, graphs and electrical networks, vibrational analysis in networked systems and random graphs. The second part deals with the study of complex networks and includes the models of "small-world", "scale-freeness", network motifs, centrality measures, the use of statistical mechanics for the analysis of networks and network communicability and the study of communities in networks. The chapter is finished by considering some dynamical models on networks, such as the consensus analysis, synchronization of coupled oscillators and epidemic models on networks.

math-ph↗

arXiv2013

About the Discriminant Power of the Subgraph Centrality and Other Centrality Measures About the Discriminant Power of the Subgraph Centrality and Other Centrality Measures(Working paper)

The discriminant power of centrality indices for the degree, eigenvector, closeness, betweenness and subgraph centrality is analyzed. It is defined by the number of graphs for which the standard deviation of the centrality of its nodes is zero. On the basis of empirical analysis it is concluded that the subgraph centrality displays better discriminant power than the rest of centralities. We also propose some new conjectures about the types of graphs for which the subgraph centrality does not discriminate among nonequivalent nodes.

cs.SI↗

arXiv2013

On d-Walk Regular Graphs

Let G be a graph with set of vertices 1,...,n and adjacency matrix A of size nxn. Let d(i,j)=d, we say that f_d:N->N is a d-function on G if for every pair of vertices i,j and k>=d, we have a_ij^(k)=f_d(k). If this function f_d exists on G we say that G is d-walk regular. We prove that G is d-walk regular if and only if for every pair of vertices i,j at distance <=d and for d<=k<=n+d-1, we have that a_ij^(k) is independent of the pair i,j. Equivalently, the single condition exp(A)*A_d=cA_d holds for some constant c, where A_d is the adjacency matrix of the d-distance graph and * denotes the Schur product.

math.CO↗

arXiv2013

A statistical mechanics description of environmental variability in metabolic networks

Many of the chemical reactions that take place within a living cell are irreversible. Due to evolutionary pressures, the number of allowable reactions within these systems are highly constrained and thus the resulting metabolic networks display considerable asymmetry. In this paper, we explore possible evolutionary factors pertaining to the reduced symmetry observed in these networks, and demonstrate the important role environmental variability plays in shaping their structural organization. Interpreting the returnability index as an equilibrium constant for a reaction network in equilibrium with a hypothetical reference system, enables us to quantify the extent to which a metabolic network is in disequilibrium. Further, by introducing a new directed centrality measure via an extension of the subgraph centrality metric to directed networks, we are able to characterise individual metabolites by their participation within metabolic pathways. To demonstrate these ideas, we study 116 metabolic networks of bacteria. In particular, we find that the equilibrium constant for the metabolic networks decreases significantly in-line with variability in bacterial habitats, supporting the view that environmental variability promotes disequilibrium within these biochemical reaction systems.

q-bio.MN↗

arXiv2013

From Integer Sequences to Block Designs via Counting Walks in Graphs

We define numbers of the type Oj(N) and Ej(N) and the corresponding integer sequences. We prove that these integer sequences, e.g., SO(N) and SE(N) correspond to the number of odd and even walks in complete graphs. We then prove that there is a unique family of graphs which have exactly the same sequence of odd walks between connected nodes and of even walks between pairs of nodes at distance two, respectively. These graphs are obtained as the Kronecker product. We show that they are the incidence graphs of block designs, are distance-regular and Ramanujan graphs.

math.CO↗

arXiv2012

Ranking hubs and authorities using matrix functions

The notions of subgraph centrality and communicability, based on the exponential of the adjacency matrix of the underlying graph, have been effectively used in the analysis of undirected networks. In this paper we propose an extension of these measures to directed networks, and we apply them to the problem of ranking hubs and authorities. The extension is achieved by bipartization, i.e., the directed network is mapped onto a bipartite undirected network with twice as many nodes in order to obtain a network with a symmetric adjacency matrix. We explicitly determine the exponential of this adjacency matrix in terms of the adjacency matrix of the original, directed network, and we give an interpretation of centrality and communicability in this new context, leading to a technique for ranking hubs and authorities. The matrix exponential method for computing hubs and authorities is compared to the well known HITS algorithm, both on small artificial examples and on more realistic real-world networks. A few other ranking algorithms are also discussed and compared with our technique. The use of Gaussian quadrature rules for calculating hub and authority scores is discussed.

math.NA↗

arXiv2012

Dynamic Network Centrality Summarizes Learning in the Human Brain

We study functional activity in the human brain using functional Magnetic Resonance Imaging and recently developed tools from network science. The data arise from the performance of a simple behavioural motor learning task. Unsupervised clustering of subjects with respect to similarity of network activity measured over three days of practice produces significant evidence of `learning', in the sense that subjects typically move between clusters (of subjects whose dynamics are similar) as time progresses. However, the high dimensionality and time-dependent nature of the data makes it difficult to explain which brain regions are driving this distinction. Using network centrality measures that respect the arrow of time, we express the data in an extremely compact form that characterizes the aggregate activity of each brain region in each experiment using a single coefficient, while reproducing information about learning that was discovered using the full data set. This compact summary allows key brain regions contributing to centrality to be visualized and interpreted. We thereby provide a proof of principle for the use of recently proposed dynamic centrality measures on temporal network data in neuroscience.

q-bio.NC↗

arXiv2011

The Physics of Communicability in Complex Networks

A fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and applied to a wide variety of real-world networks in recent years. Several such communicability functions are reviewed in this paper. It is emphasized that communication and correlation in networks can take place through many more routes than the shortest paths, a fact that may not have been sufficiently appreciated in previously proposed correlation measures. In contrast to these, the communicability measures reviewed in this paper are defined by taking into account all possible routes between two nodes, assigning smaller weights to longer ones. This point of view naturally leads to the definition of communicability in terms of matrix functions, such as the exponential, resolvent, and hyperbolic functions, in which the matrix argument is either the adjacency matrix or the graph Laplacian associated with the network. Considerable insight on communicability can be gained by modeling a network as a system of oscillators and deriving physical interpretations, both classical and quantum-mechanical, of various communicability functions. Applications of communicability measures to the analysis of complex systems are illustrated on a variety of biological, physical and social networks. The last part of the paper is devoted to a review of the notion of locality in complex networks and to computational aspects that by exploiting sparsity can greatly reduce the computational efforts for the calculation of communicability functions for large networks.

physics.soc-ph↗

arXiv2009

Topological Atomic Displacements, Kirchhoff and Wiener Indices of Molecules

We provide a physical interpretation of the Kirchhoff index of any molecules as well as of the Wiener index of acyclic ones. For the purpose, we use a local vertex invariant that is obtained from first principles and describes the atomic displacements due to small vibrations/oscillations of atoms from their equilibrium positions. In addition, we show that the topological atomic displacements correlate with the temperature factors (B-factors) of atoms obtained by X-ray crystallography for both organic molecules and biological macromolecules.

physics.chem-ph↗

arXiv2009

A Vibrational Approach to Node Centrality and Vulnerability in Complex Networks

We propose a new measure of vulnerability of a node in a complex network. The measure is based on the analogy in which the nodes of the network are represented by balls and the links are identified with springs. We define the measure as the node displacement, or the amplitude of vibration of each node, under fluctuation due to the thermal bath in which the network is supposed to be submerged. We prove exact relations among the thus defined node displacement, the information centrality and the Kirchhoff index. The relation between the first two suggests that the node displacement has a better resolution of the vulnerability than the information centrality, because the latter is the sum of the local node displacement and the node displacement averaged over the entire network.

physics.soc-ph↗