Characterizing topological and dynamical properties of complex networks without border effects

The properties of complex networks are highly Influenced by border effects frequently found as a consequence of the finite nature of real-world networks as well as network Sampling Therefore, it becomes critical to devise effective means for sound estimation of net work topological and dynamical properties will le avoiding these types of artifacts. In the current work, an algorithm for minimization of border effects is proposed and discussed, and its potential IS Illustrated with respect to two real-world networks. namely bone canals and air transportation (C) 2009 Elsevier B.V. All rights reserved.

The Missing Part of Seed Dispersal Networks: Structure and Robustness of Bat-Fruit Interactions

Mutualistic networks are crucial to the maintenance of ecosystem services. Unfortunately, what we know about seed dispersal networks is based only on bird-fruit interactions. Therefore, we aimed at filling part of this gap by investigating bat-fruit networks. It is known from population studies that: (i) some bat species depend more on fruits than others, and (ii) that some specialized frugivorous bats prefer particular plant genera. We tested whether those preferences affected the structure and robustness of the whole network and the functional roles of species. Nine bat-fruit datasets from the literature were analyzed and all networks showed lower complementary specialization (H(2)' = 0.3760.10, mean 6 SD) and similar nestedness (NODF = 0.5660.12) than pollination networks. All networks were modular (M=0.32 +/- 0.07), and had on average four cohesive subgroups (modules) of tightly connected bats and plants. The composition of those modules followed the genus-genus associations observed at population level (Artibeus-Ficus, Carollia-Piper, and Sturnira-Solanum), although a few of those plant genera were dispersed also by other bats. Bat-fruit networks showed high robustness to simulated cumulative removals of both bats (R = 0.55 +/- 0.10) and plants (R = 0.68 +/- 0.09). Primary frugivores interacted with a larger proportion of the plants available and also occupied more central positions; furthermore, their extinction caused larger changes in network structure. We conclude that bat-fruit networks are highly cohesive and robust mutualistic systems, in which redundancy is high within modules, although modules are complementary to each other. Dietary specialization seems to be an important structuring factor that affects the topology, the guild structure and functional roles in bat-fruit networks.

Generalized connectivity between any two nodes in a complex network

This article focuses on the identification of the number of paths with different lengths between pairs of nodes in complex networks and how these paths can be used for characterization of topological properties of theoretical and real-world complex networks. This analysis revealed that the number of paths can provide a better discrimination of network models than traditional network measurements. In addition, the analysis of real-world networks suggests that the long-range connectivity tends to be limited in these networks and may be strongly related to network growth and organization.

Deformed Gaussian-orthogonal-ensemble description of small-world networks

The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, random matrix theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of small world (SW) networks using an extension of the Gaussian orthogonal ensemble. This RMT ensemble, coined the deformed Gaussian orthogonal ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics until a certain range of eigenvalue correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond a certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.

Communication structure of cortical networks

Large-scale cortical networks exhibit characteristic topological properties that shape communication between brain regions and global cortical dynamics. Analysis of complex networks allows the description of connectedness, distance, clustering, and centrality that reveal different aspects of how the network's nodes communicate. Here, we focus on a novel analysis of complex walks in a series of mammalian cortical networks that model potential dynamics of information flow between individual brain regions. We introduce two new measures called absorption and driftness. Absorption is the average length of random walks between any two nodes, and takes into account all paths that may diffuse activity throughout the network. Driftness is the ratio between absorption and the corresponding shortest path length. For a given node of the network, we also define four related measurements, namely in-and out-absorption as well as in-and out-driftness, as the averages of the corresponding measures from all nodes to that node, and from that node to all nodes, respectively. We find that the cat thalamo-cortical system incorporates features of two classic network topologies, Erdos-Renyi graphs with respect to in-absorption and in-driftness, and configuration models with respect to out-absorption and out-driftness. Moreover, taken together these four measures separate the network nodes based on broad functional roles (visual, auditory, somatomotor, and frontolimbic).

Knowledge acquisition by networks of interacting agents in the presence of observation errors

In this work we investigate knowledge acquisition as performed by multiple agents interacting as they infer, under the presence of observation errors, respective models of a complex system. We focus the specific case in which, at each time step, each agent takes into account its current observation as well as the average of the models of its neighbors. The agents are connected by a network of interaction of Erdos-Renyi or Barabasi-Albert type. First, we investigate situations in which one of the agents has a different probability of observation error (higher or lower). It is shown that the influence of this special agent over the quality of the models inferred by the rest of the network can be substantial, varying linearly with the respective degree of the agent with different estimation error. In case the degree of this agent is taken as a respective fitness parameter, the effect of the different estimation error is even more pronounced, becoming superlinear. To complement our analysis, we provide the analytical solution of the overall performance of the system. We also investigate the knowledge acquisition dynamic when the agents are grouped into communities. We verify that the inclusion of edges between agents (within a community) having higher probability of observation error promotes the loss of quality in the estimation of the agents in the other communities.

Connectivity and dynamics of neuronal networks as defined by the shape of individual neurons

Biological neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of neuron shape on the overall connectivity and dynamics of the emerging networks. The current work addresses this issue by considering simplified neuronal shapes consisting of circular regions (soma/axons) with spokes (dendrites). Networks are grown by placing these patterns randomly in the two-dimensional (2D) plane and establishing connections whenever a piece of dendrite falls inside an axon. Several topological and dynamical properties of the resulting graph are measured, including the degree distribution, clustering coefficients, symmetry of connections, size of the largest connected component, as well as three hierarchical measurements of the local topology. By varying the number of processes of the individual basic patterns, we can quantify relationships between the individual neuronal shape and the topological and dynamical features of the networks. Integrate-and-fire dynamics on these networks is also investigated with respect to transient activation from a source node, indicating that long-range connections play an important role in the propagation of avalanches.

Inference of gene regulatory networks from time series by Tsallis entropy

Background: The inference of gene regulatory networks (GRNs) from large-scale expression profiles is one of the most challenging problems of Systems Biology nowadays. Many techniques and models have been proposed for this task. However, it is not generally possible to recover the original topology with great accuracy, mainly due to the short time series data in face of the high complexity of the networks and the intrinsic noise of the expression measurements. In order to improve the accuracy of GRNs inference methods based on entropy (mutual information), a new criterion function is here proposed. Results: In this paper we introduce the use of generalized entropy proposed by Tsallis, for the inference of GRNs from time series expression profiles. The inference process is based on a feature selection approach and the conditional entropy is applied as criterion function. In order to assess the proposed methodology, the algorithm is applied to recover the network topology from temporal expressions generated by an artificial gene network (AGN) model as well as from the DREAM challenge. The adopted AGN is based on theoretical models of complex networks and its gene transference function is obtained from random drawing on the set of possible Boolean functions, thus creating its dynamics. On the other hand, DREAM time series data presents variation of network size and its topologies are based on real networks. The dynamics are generated by continuous differential equations with noise and perturbation. By adopting both data sources, it is possible to estimate the average quality of the inference with respect to different network topologies, transfer functions and network sizes. Conclusions: A remarkable improvement of accuracy was observed in the experimental results by reducing the number of false connections in the inferred topology by the non-Shannon entropy. The obtained best free parameter of the Tsallis entropy was on average in the range 2.5 <= q <= 3.5 (hence, subextensive entropy), which opens new perspectives for GRNs inference methods based on information theory and for investigation of the nonextensivity of such networks. The inference algorithm and criterion function proposed here were implemented and included in the DimReduction software, which is freely available at http://sourceforge.net/projects/dimreduction and http://code.google.com/p/dimreduction/.

Exploring the random genesis of co-occurrence networks

Using the network random generation models from Gustedt (2009)[23], we simulate and analyze several characteristics (such as the number of components, the degree distribution and the clustering coefficient) of the generated networks. This is done for a variety of distributions (fixed value, Bernoulli, Poisson, binomial) that are used to control the parameters of the generation process. These parameters are in particular the size of newly appearing sets of objects, the number of contexts in which new elements appear initially, the number of objects that are shared with `parent` contexts, and, the time period inside which a context may serve as a parent context (aging). The results show that these models allow to fine-tune the generation process such that the graphs adopt properties as can be found in real world graphs. (C) 2011 Elsevier B.V. All rights reserved.

The modularity of seed dispersal: differences in structure and robustness between bat- and bird-fruit networks

In networks of plant-animal mutualisms, different animal groups interact preferentially with different plants, thus forming distinct modules responsible for different parts of the service. However, what we currently know about seed dispersal networks is based only on birds. Therefore, we wished to fill this gap by studying bat-fruit networks and testing how they differ from bird-fruit networks. As dietary overlap of Neotropical bats and birds is low, they should form distinct mutualistic modules within local networks. Furthermore, since frugivory evolved only once among Neotropical bats, but several times independently among Neotropical birds, greater dietary overlap is expected among bats, and thus connectance and nestedness should be higher in bat-fruit networks. If bat-fruit networks have higher nestedness and connectance, they should be more robust to extinctions. We analyzed 1 mixed network of both bats and birds and 20 networks that consisted exclusively of either bats (11) or birds (9). As expected, the structure of the mixed network was both modular (M = 0.45) and nested (NODF = 0.31); one module contained only birds and two only bats. In 20 datasets with only one disperser group, bat-fruit networks (NODF = 0.53 +/- A 0.09, C = 0.30 +/- A 0.11) were more nested and had a higher connectance than bird-fruit networks (NODF = 0.42 +/- A 0.07, C = 0.22 +/- A 0.09). Unexpectedly, robustness to extinction of animal species was higher in bird-fruit networks (R = 0.60 +/- A 0.13) than in bat-fruit networks (R = 0.54 +/- A 0.09), and differences were explained mainly by species richness. These findings suggest that a modular structure also occurs in seed dispersal networks, similar to pollination networks. The higher nestedness and connectance observed in bat-fruit networks compared with bird-fruit networks may be explained by the monophyletic evolution of frugivory in Neotropical bats, among which the diets of specialists seem to have evolved from the pool of fruits consumed by generalists.

The nested assembly of individual-resource networks

P>1. Much of the current understanding of ecological systems is based on theory that does not explicitly take into account individual variation within natural populations. However, individuals may show substantial variation in resource use. This variation in turn may be translated into topological properties of networks that depict interactions among individuals and the food resources they consume (individual-resource networks). 2. Different models derived from optimal diet theory (ODT) predict highly distinct patterns of trophic interactions at the individual level that should translate into distinct network topologies. As a consequence, individual-resource networks can be useful tools in revealing the incidence of different patterns of resource use by individuals and suggesting their mechanistic basis. 3. In the present study, using data from several dietary studies, we assembled individual-resource networks of 10 vertebrate species, previously reported to show interindividual diet variation, and used a network-based approach to investigate their structure. 4. We found significant nestedness, but no modularity, in all empirical networks, indicating that (i) these populations are composed of both opportunistic and selective individuals and (ii) the diets of the latter are ordered as predictable subsets of the diets of the more opportunistic individuals. 5. Nested patterns are a common feature of species networks, and our results extend its generality to trophic interactions at the individual level. This pattern is consistent with a recently proposed ODT model, in which individuals show similar rank preferences but differ in their acceptance rate for alternative resources. Our findings therefore suggest a common mechanism underlying interindividual variation in resource use in disparate taxa.

Comparison of the interactomic networks of different species in terms of accessibility

Protein-protein interaction networks were investigated in terms of outward accessibility, which quantifies the effectiveness of each protein in accessing other proteins and is related to the internality of nodes. By comparing the accessibility between 144 ortholog proteins in yeast and the fruit fly, we found that the accessibility tends to be higher among proteins in the fly than in yeast. In addition, z-scores of the accessibility calculated for different species revealed that the protein networks of less evolved species tend to be more random than those of more evolved species. The accessibility was also used to identify the border of the yeast protein interaction network, which was found to be mainly composed of viable proteins.

Modeling worldwide highway networks

This Letter addresses the problem of modeling the highway systems of different countries by using complex networks formalism. More specifically, we compare two traditional geographical models with a modified geometrical network model where paths, rather than edges, are incorporated at each step between the origin and the destination vertices. Optimal configurations of parameters are obtained for each model and used for the comparison. The highway networks of Australia, Brazil, India, and Romania are considered and shown to be properly modeled by the modified geographical model. (C) 2009 Elsevier B.V. All rights reserved.

Investigating relationships within and between category networks in Wikipedia

This work maps and analyses cross-citations in the areas of Biology, Mathematics, Physics and Medicine in the English version of Wikipedia, which are represented as an undirected complex network where the entries correspond to nodes and the citations among the entries are mapped as edges. We found a high value of clustering coefficient for the areas of Biology and Medicine, and a small value for Mathematics and Physics. The topological organization is also different for each network, including a modular structure for Biology and Medicine, a sparse structure for Mathematics and a dense core for Physics. The networks have degree distributions that can be approximated by a power-law with a cut-off. The assortativity of the isolated networks has also been investigated and the results indicate distinct patterns for each subject. We estimated the betweenness centrality of each node considering the full Wikipedia network, which contains the nodes of the four subjects and the edges between them. In addition, the average shortest path length between the subjects revealed a close relationship between the subjects of Biology and Physics, and also between Medicine and Physics. Our results indicate that the analysis of the full Wikipedia network cannot predict the behavior of the isolated categories since their properties can be very different from those observed in the full network. (C) 2011 Elsevier Ltd. All rights reserved.

A complex network approach to text summarization

Automatic summarization of texts is now crucial for several information retrieval tasks owing to the huge amount of information available in digital media, which has increased the demand for simple, language-independent extractive summarization strategies. In this paper, we employ concepts and metrics of complex networks to select sentences for an extractive summary. The graph or network representing one piece of text consists of nodes corresponding to sentences, while edges connect sentences that share common meaningful nouns. Because various metrics could be used, we developed a set of 14 summarizers, generically referred to as CN-Summ, employing network concepts such as node degree, length of shortest paths, d-rings and k-cores. An additional summarizer was created which selects the highest ranked sentences in the 14 systems, as in a voting system. When applied to a corpus of Brazilian Portuguese texts, some CN-Summ versions performed better than summarizers that do not employ deep linguistic knowledge, with results comparable to state-of-the-art summarizers based on expensive linguistic resources. The use of complex networks to represent texts appears therefore as suitable for automatic summarization, consistent with the belief that the metrics of such networks may capture important text features. (c) 2008 Elsevier Inc. All rights reserved.