# American Institute of Mathematical Sciences

ISSN:
1556-1801

eISSN:
1556-181X

All Issues

## Networks & Heterogeneous Media

March 2015 , Volume 10 , Issue 1

Special issue on new trends, models and applications in complex and multiplex networks

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2015, 10(1): i-iii doi: 10.3934/nhm.2015.10.1i +[Abstract](3717) +[PDF](156.8KB)
Abstract:
The real world surrounding us is full of complex systems from various types and categories. Internet, the World Wide Web, biological and biochemical networks (brain, metabolic, protein and genomic networks), transport networks (underground, train, airline networks, road networks), communication networks (computer servers, Internet, online social networks), and many others (social community networks, electric power grids and water supply networks,...) are a few examples of the many existing kinds and types of networks [1,2,3,4,6,8,9,10,11]. In the recent past years, the study of structure and dynamics of complex networks has been the subject of intense interest. Recent advances in the study of complex networked systems has put the spotlight on the existence of more than one type of links whose interplay can affect the structure and function of those systems [5,7]. In these networks, relevant information may not be captured if the single layers are analyzed separately, since these different components and units interact with others through different channels of connectivity and dependencies. The global characteristics and behavior of these systems depend on multiple dimensions of integration, relationship or cleavage of its units.

2015, 10(1): 1-16 doi: 10.3934/nhm.2015.10.1 +[Abstract](3472) +[PDF](444.0KB)
Abstract:
We analyze the transferability of collective transportation line networks (CTLN) with the help of hypergraphs, their linearization, and connectivity measures from Complex Network Theory. In contrast to other existing works in the literature, where transferability is analyzed at a topological level, we are also concerned with passenger system level, introducing data on the travel patterns. This will allow us to have a more complete view of the functioning of the transfer system of a CTLN.
2015, 10(1): 17-35 doi: 10.3934/nhm.2015.10.17 +[Abstract](5341) +[PDF](993.6KB)
Abstract:
In this work we present a new approach for co-authorship link prediction based on leveraging information contained in general bibliographical multiplex networks. A multiplex network is a graph defined over a set of nodes linked by different types of relations. For instance, the multiplex network we are studying here is defined as follows : nodes represent authors and links can be one of the following types: co-authorship links, co-venue attending links and co-citing links. A supervised-machine learning based link prediction approach is applied. A link formation model is learned based on a set of topological attributes describing both positive and negative examples. While such an approach has been successfully applied in the context on simple networks, different options can be applied to extend it to multiplex networks. One option is to compute topological attributes in each layer of the multiplex. Another one is to compute directly new multiplex-based attributes quantifying the multiplex nature of dyads (potential links). These different approaches are studied and compared through experiments on real datasets extracted from the bibliographical database DBLP.
2015, 10(1): 37-52 doi: 10.3934/nhm.2015.10.37 +[Abstract](5219) +[PDF](10220.5KB)
Abstract:
Mutualistic networks are considered an example of resilience against perturbations. Mutualistic interactions are beneficial for the two sets of species involved. Network robustness has been usually measured in terms of extinction sequences, i.e., nodes are removed from the empirical bipartite network one subset (primary extinctions) and the number of extinctions on the other subset (secondary extinction) is computed. This is a first approach to study ecosystems extinction. However, each interacting species, depicted as a node of the mutualistic network, is really composed by certain number of individuals (population) and its shortage can diminish dramatically the population of its interacting partners, i.e. the population dynamics plays an important role in the robustness of the ecological networks. Although different models of population dynamics for mutualistic interacting species have been addressed, like Type II models, only recently a new mutualistic model has been proposed exhibiting bounded solutions and good properties for simulation. In this paper we show that population dynamics is as important as network topology when we are interested in the resilience of the community.
2015, 10(1): 53-70 doi: 10.3934/nhm.2015.10.53 +[Abstract](6013) +[PDF](1626.2KB)
Abstract:
Dynamic population models are based on the Verhulst's equation (logisitic equation), where the classic Malthusian growth rate is damped by intraspecific competition terms. Mainstream population models for mutualism are modifications of the logistic equation with additional terms to account for the benefits produced by the interspecies interactions. These models have shortcomings as the population divergence under some conditions (May's equations) or a mathematical complexity that difficults their analytical treatment (Wright's type II models). In this work, we introduce a model for the population dynamics in mutualism inspired by the logistic equation but cured of divergences. The model is also mathematically more simple than the type II. We use numerical simulations to study the model stability in more general interaction scenarios. Despite its simplicity, our results suggest that the model dynamics are rich and may be used to gain further insights in the dynamics of mutualistic interactions.
2015, 10(1): 71-85 doi: 10.3934/nhm.2015.10.71 +[Abstract](4648) +[PDF](709.4KB)
Abstract:
Multiplex network is an emergent model that has been lately proposed in order to cope with the complexity of real-world networks. A multiplex network is defined as a multi-layer interconnected graph. Each layer contains the same set of nodes but interconnected by different types of links. This rich representation model requires to redefine most of the existing network analysis algorithms. In this paper we focus on the central problem of community detection. Most of existing approaches consist on transforming the problem, in a way or another, to the classical setting of community detection in a monoplex network. In this work, we propose a new approach that consists on adapting a seed-centric algorithm to the multiplex case. The first experiments on heterogeneous bibliographical networks show the relevance of the approach compared to the existing algorithms.
2015, 10(1): 87-99 doi: 10.3934/nhm.2015.10.87 +[Abstract](3811) +[PDF](2756.0KB)
Abstract:
Towards the consolidation of peace and national development, Ivory Coast must overcome the lack of cohesion, responsible for the emergence of two civil wars in the last years. As in many African countries, ethnic violence is a result of the way territories are organized and the prevalence of some groups over others. Nowadays the increasing availability of electronic data allows to quantify and unveil societal relationships in an unprecedented way. In this sense, the present work analyzes mobile phone data in order to provide information about the regional and ethnic interactions in Ivory Coast. We accomplish so by means of the construction and analysis of complex social networks with several types of interactions, such as calling activity and human mobility. We found that in a subregional scale, the ethnic identity plays an important role in the communication patterns, while at the interregional scale, other factors arise like economical interests and available infrastructure.
2015, 10(1): 101-125 doi: 10.3934/nhm.2015.10.101 +[Abstract](3254) +[PDF](1788.8KB)
Abstract:
In this paper we extend the concept of Competitivity Graph to compare series of rankings with ties ( partial rankings). We extend the usual method used to compute Kendall's coefficient for two partial rankings to the concept of evolutive Kendall's coefficient for a series of partial rankings. The theoretical framework consists of a four-layer multiplex network. Regarding the treatment of ties, our approach allows to define a tie between two values when they are close enough, depending on a threshold. We show an application using data from the Spanish Stock Market; we analyse the series of rankings defined by $25$ companies that have contributed to the IBEX-35 return and volatility values over the period 2003 to 2013.
2015, 10(1): 127-148 doi: 10.3934/nhm.2015.10.127 +[Abstract](3642) +[PDF](842.9KB)
Abstract:
As the framework to characterize the subway and urban bus networks of Madrid city three topological spaces: geographical stop space, transfer space and route space, are considered. We show that the subway network exhibits better structural parameters than the urban bus network, with higher performance since in average a stop is reachable passing through less number of stops and carrying out less number of transfers between lines. We have found that the cumulative degree distributions of the subway and urban bus networks correspond to an exponential function, while the degree-degree correlations present a power law distributions in both transport systems. The relationship between transport flows and population are also studied at the city level by analyzing the flow between all the district (administrative areas) of Madrid. We prove that these flows can be described by a Gravity Model which takes into account the population from the origin and destination districts as well as the number of sections of a transport line that passes through two different districts.
2015, 10(1): 149-165 doi: 10.3934/nhm.2015.10.149 +[Abstract](3254) +[PDF](1224.3KB)
Abstract:
We address the problem of gauging the influence exerted by a given country on the international trade market from the viewpoint of complex networks. In particular, we apply the PWP method to compute indirect influences on the world trade network.
2015, 10(1): 167-194 doi: 10.3934/nhm.2015.10.167 +[Abstract](3034) +[PDF](7226.2KB)
Abstract:
In this work we analyzed the relationships between powerful politicians and businessmen of Chile in order to study the phenomenon of social power. We developed our study according to Complex Network Theory but also using traditional sociological theories of Power and Elites. Our analyses suggest that the studied network displays common properties of Complex Networks, such as scaling in connectivity distribution, properties of small-world networks, and modular structure, among others. We also observed that social power (a proposed metric is presented in this work) is also distributed inhomogeneously. However, the most interesting observation is that this inhomogeneous power and connectivity distribution, among other observed properties, may be the result of a dynamic and unregulated process of network growth in which powerful people tend to link to similar others. The compatibility between people, increasingly selective as the network grows, could generate the presence of extremely powerful people, but also a constant inequality of power where the difference between the most powerful is the same as among the least powerful. Our results are also in accordance with sociological theories.
2015, 10(1): 195-208 doi: 10.3934/nhm.2015.10.195 +[Abstract](3115) +[PDF](393.1KB)
Abstract:
In this work we propose a model for the diffusion of information in a complex network. The main assumption of the model is that the information is initially located at certain nodes and then is disseminated, with occasional losses when traversing the edges, to the rest of the network. We present two efficient algorithms, which we called max-path and sum-path, to compute, respectively, lower and upper bounds for the amount of information received at each node. Finally we provide an application of these algorithms to intentional risk analysis.
2015, 10(1): 209-221 doi: 10.3934/nhm.2015.10.209 +[Abstract](2948) +[PDF](7581.7KB)
Abstract:
We report a systematic investigation of the magnetic anisotropy effects observed in the deterministic spin dynamics of a magnetic particle in the presence of a time-dependent magnetic field. The system is modeled by the Landau-Lifshitz-Gilbert equation and the magnetic field consists of two terms, a constant term and a term involving a harmonic time modulation. We consider a general quadratic anisotropic energy with three different preferential axes. The dynamical behavior of the system is represented in Lyapunov phase diagrams, and by calculating bifurcation diagrams, Poincaré sections and Fourier spectra. We find an intricate distribution of shrimp-shaped regular island embedded in wide chaotic phases. Anisotropy effects are found to play a key role in defining the symmetries of regular and chaotic stability phases.
2015, 10(1): 223-232 doi: 10.3934/nhm.2015.10.223 +[Abstract](2952) +[PDF](1143.2KB)
Abstract:
Functional connectivity in human brain can be represented as a network using electroencephalography (EEG) signals. Network representation of EEG time series can be an efficient vehicle to understand the underlying mechanisms of brain function. Brain functional networks whose nodes are brain regions and edges correspond to functional links between them are characterized by neurobiologically meaningful graph theory metrics. This study investigates the degree to which graph theory metrics are sex dependent. To this end, EEGs from 24 healthy female subjects and 21 healthy male subjects were recorded in eyes-closed resting state conditions. The connectivity matrices were extracted using correlation analysis and were further binarized to obtain binary functional networks. Global and local efficiency measures as graph theory metrics were computed for the extracted networks. We found that male brains have significantly greater global efficiency (i.e., global communicability of the network) across all frequency bands for a wide range of cost values in both hemispheres. Furthermore, for a range of cost values, female brains showed significantly greater right-hemispheric local efficiency (i.e., local connectivity) than male brains.

2020 Impact Factor: 1.213
5 Year Impact Factor: 1.384
2020 CiteScore: 1.9