Showing papers on "Weighted network published in 2007"

Structure and tie strengths in mobile communication networks

Abstract: ncovering the structure and function of communication networks has always been constrained by the practical difficulty of mapping out interactions among a large number of individuals. Indeed, most of our current understanding of com- munication and social networks is based on questionnaire data, reaching typically a few dozen individuals and relying on the individual's opinion to reveal the nature and the strength of the ties. The fact that currently an increasing fraction of human interactions are recorded, from e-mail (1-3) to phone records (4), offers unprecedented opportunities to uncover and explore the large scale characteristics of communication and social networks (5). Here we take a first step in this direction by exploiting the widespread use of mobile phones to construct a map of a society-wide communication network, capturing the mobile interaction patterns of millions of individuals. The data set allows us to explore the relationship between the topology of the network and the tie strengths between individuals, informa- tion that was inaccessible at the societal level before. We demonstrate a local coupling between tie strengths and network topology, and show that this coupling has important conse- quences for the network's global stability if ties are removed, as well as for the spread of news and ideas within the network. A significant portion of a country's communication network wasreconstructedfrom18weeksofallmobilephonecallrecords among 20% of the country's entire population, 90% of whose

Meeting Strangers and Friends of Friends: How Random are Social Networks?

Abstract: We present a dynamic model of network formation where nodes find other nodes with whom to form links in two ways: some are found uniformly at random, while others are found by searching locally through the current structure of the network (e.g., meeting friends of friends). This combination of meeting processes results in a spectrum of features exhibited by large social networks, including the presence of more high- and low-degree nodes than when links are formed independently at random, having low distances between nodes in the network, and having high clustering of links on a local level. We fit the model to data from six networks and impute the relative ratio of random to network-based meetings in link formation, which turns out to vary dramatically across applications. We show that as the random/network-based meeting ratio varies, the resulting degree distributions can be ordered in the sense of stochastic dominance, which allows us to infer how the formation process affects average utility in the network.

Generalizations of the clustering coefficient to weighted complex networks

Abstract: The recent high level of interest in weighted complex networks gives rise to a need to develop new measures and to generalize existing ones to take the weights of links into account. Here we focus on various generalizations of the clustering coefficient, which is one of the central characteristics in the complex network theory. We present a comparative study of the several suggestions introduced in the literature, and point out their advantages and limitations. The concepts are illustrated by simple examples as well as by empirical data of the world trade and weighted coauthorship networks.

Analysis of a large-scale weighted network of one-to-one human communication

Abstract: We construct a connected network of 3.9 million nodes from mobile phone call records, which can be regarded as a proxy for the underlying human communication network at the societal level. We assign two weights on each edge to reflect the strength of social interaction, which are the aggregate call duration and the cumulative number of calls placed between the individuals over a period of 18 weeks. We present a detailed analysis of this weighted network by examining its degree, strength, and weight distributions, as well as its topological assortativity and weighted assortativity, clustering and weighted clustering, together with correlations between these quantities. We give an account of motif intensity and coherence distributions and compare them to a randomized reference system. We also use the concept of link overlap to measure the number of common neighbours any two adjacent nodes have, which serves as a useful local measure for identifying the interconnectedness of communities. We report a positive correlation between the overlap and weight of a link, thus providing

Emergence of communities in weighted networks.

Abstract: Topology and weights are closely related in weighted complex networks and this is reflected in their modular structure. We present a simple network model where the weights are generated dynamically and they shape the developing topology. By tuning a model parameter governing the importance of weights, the resulting networks undergo a gradual structural transition from a module-free topology to one with communities. The model also reproduces many features of large social networks, including the "weak links" property.

Detecting complex network modularity by dynamical clustering

Abstract: Based on cluster desynchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and real-world networks whose modular structure is already known or has been studied by means of other methods. The algorithm attains a high level of precision, especially when the modular units are very mixed and hardly detectable by the other methods, with a computational effort O(KN) on a generic graph with N nodes and K links.

The Structure of Interurban Traffic: A Weighted Network Analysis:

Abstract: We study the structure of the network representing the interurban commuting traffic of the Sardinia region, Italy, which amounts to 375 municipalities and 1600 000 inhabitants. We use a weighted ne...

Weighted network modules

Abstract: The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of real- world webs. We introduce a clustering algorithm clique percolation method with weights (CPMw) for weighted networks based on the concept of percolating k-cliques with high enough intensity. The algorithm allows overlaps between the modules. First, we give detailed analytical and numerical results about the critical point of weighted k-clique percolation on (weighted) Erdý os-Renyi graphs. Then, for a scientist collaboration web and a stock correlation graph we compute three-link weight correlations and with the CPMw the weighted modules. After reshuffling link weights in both networks and computing the same quantities for the randomized control graphs as well, we show that groups of three or more strong links prefer to cluster together in both original graphs.

Complex network analysis of free-energy landscapes.

Abstract: The kinetics of biomolecular isomerization processes, such as protein folding, is governed by a free-energy surface of high dimensionality and complexity. As an alternative to projections into one or two dimensions, the free-energy surface can be mapped into a weighted network where nodes and links are configurations and direct transitions among them, respectively. In this work, the free-energy basins and barriers of the alanine dipeptide are determined quantitatively using an algorithm to partition the network into clusters (i.e., states) according to the equilibrium transitions sampled by molecular dynamics. The network-based approach allows for the analysis of the thermodynamics and kinetics of biomolecule isomerization without reliance on arbitrarily chosen order parameters. Moreover, it is shown on low-dimensional models, which can be treated analytically, as well as for the alanine dipeptide, that the broad-tailed weight distribution observed in their networks originates from free-energy basins with mainly enthalpic character.

Patterns of dominant flows in the world trade web

Abstract: The large-scale organization of the world economies is exhibiting increasing levels of local heterogeneity and global interdependency. Understanding the relation between local and global features calls for analytical tools able to uncover the global emerging organization of the international trade network. Here we analyze the world network of bilateral trade imbalances and characterize its overall flux organization, unraveling local and global high-flux pathways that define the backbone of the trade system. We develop a general procedure capable to progressively filter out in a consistent and quantitative way the dominant trade channels. This procedure is completely general and can be applied to any weighted network to detect the underlying structure of transport flows. The trade fluxes properties of the world trade web determine a ranking of trade partnerships that highlights global interdependencies, providing information not accessible by simple local analysis. The present work provides new quantitative tools for a dynamical approach to the propagation of economic crises.

Patterns of dominant flows in the world trade web

Abstract: The large-scale organization of the world economies is exhibiting increasingly levels of local heterogeneity and global interdependency. Understanding the relation between local and global features calls for analytical tools able to uncover the global emerging organization of the international trade network. Here we analyze the world network of bilateral trade imbalances and characterize its overall flux organization, unraveling local and global high-flux pathways that define the backbone of the trade system. We develop a general procedure capable to progressively filter out in a consistent and quantitative way the dominant trade channels. This procedure is completely general and can be applied to any weighted network to detect the underlying structure of transport flows. The trade fluxes properties of the world trade web determines a ranking of trade partnerships that highlights global interdependencies, providing information not accessible by simple local analysis. The present work provides new quantitative tools for a dynamical approach to the propagation of economic crises.

Scaling and correlations in three bus-transport networks of China

Abstract: We report the statistical properties of three bus-transport networks (BTN) in three different cities of China. These networks are composed of a set of bus lines and stations serviced by these. Network properties, including the degree distribution, clustering and average path length are studied in different definitions of network topology. We explore scaling laws and correlations that may govern intrinsic features of such networks. Besides, we create a weighted network representation for BTN with lines mapped to nodes and number of common stations to weights between lines. In such a representation, the distributions of degree, strength and weight are investigated. A linear behavior between strength and degree s ( k ) ∼ k is also observed.

Networks of strong ties

Abstract: Social networks transmitting covert or sensitive information cannot use all ties for this purpose. Rather, they can only use a subset of ties that are strong enough to be “trusted”. This paper addresses whether it is still possible, under this restriction, for information to be transmitted widely and rapidly in social networks. We use transitivity as evidence of strong ties, requiring one or more shared contacts in order to count an edge as strong. We examine the effect of removing all non-transitive ties in two real social network data sets, imposing varying thresholds in the number of shared contacts. We observe that transitive ties occupy a large portion of the network and that removing all other ties, while causing some individuals to become disconnected, preserves the majority of the giant connected component. Furthermore, the average shortest path, important for the rapid diffusion of information, increases only slightly relative to the original network. We also evaluate the cost of forming transitive ties by modeling a random graph composed entirely of closed triads and comparing its connectivity and average shortest path with the equivalent Erdos–Renyi random graph. Both the empirical study and random model point to a robustness of strong ties with respect to the connectivity and small world property of social networks.

Weighted assortative and disassortative networks model

Abstract: Real-world networks process structured connections since they have non-trivial vertex degree correlation and clustering. Here we propose a toy model of structure formation in real-world weighted network. In our model, a network evolves by topological growth as well as by weight change. In addition, we introduce the weighted assortativity coefficient, which generalizes the assortativity coefficient of a topological network, to measure the tendency of having a high-weighted link between two vertices of similar degrees. Network generated by our model exhibits scale-free behavior with a tunable exponent. Besides, a few non-trivial features found in real-world networks are reproduced by varying the parameter ruling the speed of weight evolution. Most importantly, by studying the weighted assortativity coefficient, we found that both topologically assortative and disassortative networks generated by our model are in fact weighted assortative.

Self-organization versus hierarchy in open-source social networks.

Abstract: Complex networks emerge under different conditions including design (i.e., top-down decisions) through simple rules of growth and evolution. Such rules are typically local when dealing with biological systems and most social webs. An important deviation from such a scenario is provided by groups, collectives of agents engaged in technology development, such as open-source communities. Here we analyze their network structure, showing that it defines a complex weighted network with scaling laws at different levels, as measured by looking at e-mail exchanges. We also present a simple model of network growth involving nonlocal rules based on betweenness centrality. Our weighted network analysis suggests that a well-defined interplay between the overall goals of the community and the underlying hierarchical organization play a key role in shaping its dynamics.

Clusters or networks of economies? A macroeconomy study through Gross Domestic Product

Abstract: We study correlations between web-downloaded gross domestic product (GDP)’s of rich countries. GDP is used as wealth signatures of the country economical state. We calculate the yearly fluctuations of the GDP. We look for forward and backward correlations between such fluctuations. The correlation measure is based on the Theil index. The system is represented by an evolving weighted network, nodes being the GDP fluctuations (or countries) at different times. In order to extract structures from the network, we focus on filtering the time delayed correlations by removing the least correlated links. This percolation idea-based method reveals the emergence of connections, that are visualized by a branching representation. Note that the network is made of weighted and directed links when taking into account a delay time. Such a measure of collective habits does not readily fit the usual expectations, except if an economy globalization framework is accepted. r 2007 Published by Elsevier B.V.

Ensemble approach to the analysis of weighted networks.

Abstract: We present an approach to the analysis of weighted networks, by providing a straightforward generalization of any network measure defined on unweighted networks, such as the average degree of the nearest neighbors, the clustering coefficient, the "betweenness," the distance between two nodes, and the diameter of a network. All these measures are well established for unweighted networks but have hitherto proven difficult to define for weighted networks. Our approach is based on the translation of a weighted network into an ensemble of edges. Further introducing this approach we demonstrate its advantages by applying the clustering coefficient constructed in this way to two real-world weighted networks.

System and method for facilitating accelerated network selection using a weighted network list

Abstract: A scheme for facilitating accelerated network selection by a wireless user equipment (UE) device. In one exemplary embodiment, prior to performing a full band scan, the wireless UE device is operable to interrogate a list of networks with which the wireless UE device has registered at least once in a given period of time, wherein a network availability likelihood score may be associated with each of the list of networks. A particular network is selected from the list of networks based on its network availability likelihood score.

How to become a superhero

Abstract: We analyze a collaboration network based on the Marvel Universe comic books. First, we consider the system as a binary network, where two characters are connected if they appear in the same publication. The analysis of degree correlations reveals that, in contrast to most real social networks, the Marvel Universe presents a disassortative mixing on the degree. Then, we use a weight measure to study the system as a weighted network. This allows us to find and characterize well defined communities. Through the analysis of the community structure and the clustering as a function of the degree we show that the network presents a hierarchical structure. Finally, we comment on possible mechanisms responsible for the particular motifs observed.

Weighted network properties of Chinese nature science basic research

Abstract: Using the requisition papers of Chinese Nature Science Basic Research in management and information department, we construct the weighted network of research areas (WNRA). In WNRA, two research areas, which is represented by the subject codes, are considered to be connected if they have been filled in one or more requisition papers. The edge weight is defined as the number of requisition papers which have been filled in the same pairs of codes. The node strength is defined as the number of requisition papers which have been filled in this code, including the papers which have been filled in it alone. Here we study a variety of nonlocal statistics for WNRA, such as typical distance between research areas and measure of centrality such as betweenness. These statistical characteristics can illuminate the global development trend of Chinese scientific study. It is also helpful to adjust the code system to reflect the real status more accurately. Finally, we present a plausible model for the formation and structure of WNRA with the observed properties.

The effect of weight on community structure of networks

Abstract: The effect of weight on community structures is investigated in this paper. We use weighted modularity Q w to evaluate the partitions and weighted extremal optimization algorithm to detect communities. Starting from empirical and idealized weighted networks, the matching between weights and edges are disturbed. Then using similarity function S to measure the difference between community structures, it is found that the redistribution of weights does strongly affect the community structure especially in dense networks. This indicates that the community structure in networks is a suitable property to reflect the role of weight.

Empirical analysis of the ship-transport network of China.

Abstract: Structural properties of the ship-transport network of China (STNC) are studied in the light of recent investigations of complex networks. STNC is composed of a set of routes and ports located along the sea or river. Network properties including the degree distribution, degree correlations, clustering, shortest path length, centrality, and betweenness are studied in different definitions of network topology. It is found that geographical constraint plays an important role in the network topology of STNC. We also study the traffic flow of STNC based on the weighted network representation, and demonstrate the weight distribution can be described by power-law or exponential function depending on the assumed definition of network topology. Other features related to STNC are also investigated.

The role of edge weights in social networks: modelling structure and dynamics

Abstract: The structure of social networks influences dynamic processes of human interaction and communication, such as opinion formation and spreading of information or infectious diseases. To facilitate simulation studies of such processes, we have developed a weighted network model to resemble the structure of real social networks, in particular taking into account recent observations on weight-topology correlations. The model iterates on a fixed size network, reaching a steady state through processes of weighted local searches, global random attachment, and random deletion of nodes. There are essentially two parameters which can be used to tune network properties. The generated networks display community structure, with strong internal links and weak links connecting the communities. Similarly to empirical observations, strong ties correlate with overlapping neighbourhoods, and under edge removal, the network becomes fragmented faster when weak ties are removed first. As an example of the effects that such structural properties have on dynamic processes, we present early results from studies of social dynamics describing the competition of two non-excluding opinions in a society, showing that the weighted community structure slows down the dynamics as compared to randomized references.

The structure of weighted small-world networks

Abstract: The small-world property, vertices are highly clustered yet the path length between them is small, has been widely studied in unweighted graphs. In many real-world networks, the connections have associated weights that represent the strength of the interactions among vertices. This important feature, however, has not drawn a lot of attention until recently because the weighted networks are more difficult to analyze than their unweighted counterparts. In this study, the structure of the weighted small-world networks is investigated. Two weighted scientific collaboration networks, whose unweighted versions have been shown to have small-world properties, were analyzed. We generalized the clustering coefficient, and the average shortest path to combine the weight and the topological structure of the network. Furthermore, the nested community structure was also studied. By zooming in the small-world networks, we showed that the sub-networks are still small-world networks.

Clusters in weighted macroeconomic networks : the EU case. Introducing the overlapping index of GDP/capita fluctuation correlations

Abstract: GDP/capita correlations are investigated in various time windows (TW), for the time interval 1990-2005. The target group of countries is the set of 25 EU members, 15 till 2004 plus the 10 countries which joined EU later on. The TW-means of the statistical correlation coefficients are taken as the weights (links) of a fully connected network having the countries as nodes. Thereafter we define and introduce the overlapping index of weighted network nodes. A cluster structure of EU countries is derived from the statistically relevant eigenvalues and eigenvectors of the adjacency matrix. This may be considered to yield some information about the structure, stability and evolution of the EU country clusters in a macroeconomic sense.

How Difficult is it to Develop a Perfect Spell-checker? A Cross-Linguistic Analysis through Complex Network Approach

Abstract: The difficulties involved in spelling error detection and correction in a language have been investigated in this work through the conceptualization of SpellNet ‐ the weighted network of words, where edges indicate orthographic proximity between two words. We construct SpellNets for three languages - Bengali, English and Hindi. Through appropriate mathematical analysis and/or intuitive justification, we interpret the different topological metrics of SpellNet from the perspective of the issues related to spell-checking. We make many interesting observations, the most significant among them being that the probability of making a real word error in a language is propotionate to the average weighted degree of SpellNet, which is found to be highest for Hindi, followed by Bengali and English.

Managing network risk via critical node identification

Abstract: We consider methodologies for managing risk in a telecommunication net- work based on identification of the critical nodes. The objec tive is to identify a set of vertices with a specified cardinality whose deletion result s is maximum number of discon- nected components. This is referred to as the CRITICAL NODE PROBLEM, and finds ap- plication in epidemic control, telecommunications, and military tactical planning, among others. From a telecommunication perspective, the set of critical nodes helps determine which players should be removed from the network in the event of a virus outbreak. Con- versely, in order to maintain maximum global connectivity, it should be ensured that the critical nodes remain intact. In this chapter, we review the recent work in this area and examine formulations based on integer linear programming. In this chapter, we study two variants of the CRITICAL NODE PROBLEM. In general, the objective of the CRITICAL NODE PROBLEM (CNP) is to find a set of k nodes in a graph whose deletion results in the maximum network fragmentation. By this we mean, maximize the number of components in thek-vertex deleted subgraph. Studies carried out in this line include those by Bavelas (6) and Freeman (15) which emphasize node centrality and prestige, both of which are usually functions of a nodes degree. However, they lacked applications to problems which emphasized network fragmentation and connectivity. We can apply the CNP to the problem of jamming wired telecommunication networks by identifying the critical nodes and suppressing the communication on these nodes. This will result in the maximum number of disconnected components which are unable to communi- cate with each other. The CNP can also be applied to the study of covert terrorist networks , where a certain number of individuals have to be identified wh ose deletion would result in the maximum breakdown of communication between individuals in the network (24). Likewise in order to stop the spreading of a virus over a telecommunication network, one can identify the critical nodes of the graph and take them offl ine. The CNP also finds applications in network immunization (9, 34) wher e mass vaccina- tion is an expensive process and only a specific number of peop le, modeled as nodes of a graph, can be vaccinated. The immunized nodes cannot propagate the virus and the goal is to identify the individuals to be vaccinated in order to redu ce the overall transmissibility of the virus. There are several vaccination strategies in the l iterature (see e.g. (9, 34)) offering control of epidemic outbreaks; however, none of the proposed are optimal strategies. The vaccination strategies suggested emphasize the centrality of nodes as a major factor rather than critical nodes whose deletion will maximize disconnectivity of the graph. Deletion of central nodes may not guarantee a fragmentation of the network or even disconnectivity, in which case disease transmission cannot be prevented. Of course, owing to its dynamic stature, the relationships between people, represented by edges in the social network are transient and there is a constant rewiring between nodes, and alternate relationships could

The International Trade Network: weighted network analysis and modelling

Abstract: Tools of the theory of critical phenomena, namely the scaling analysis and universality, are argued to be applicable to large complex web-like network structures. Using a detailed analysis of the real data of the International Trade Network we argue that the scaled link weight distribution has an approximate log-normal distribution which remains robust over a period of 53 years. Another universal feature is observed in the power-law growth of the trade strength with gross domestic product, the exponent being similar for all countries. Using the 'rich-club' coefficient measure of the weighted networks it has been shown that the size of the rich-club controlling half of the world's trade is actually shrinking. While the gravity law is known to describe well the social interactions in the static networks of population migration, international trade, etc, here for the first time we studied a non-conservative dynamical model based on the gravity law which excellently reproduced many empirical features of the ITN.

QoSMap: QoS aware Mapping of Virtual Networks for Resiliency and Efficiency

Abstract: We describe QoSMap, an efficient and flexible mechanism for constructing virtual networks on a shared Internet substrate for applications having stringent QoS and resiliency requirements. Applications specify desired overlay topology and weighted network characteristics which serve as resource constraints desired by the application in meeting the QoS expectations. QoSMap uses these constraints to select an overlay consisting of high quality direct paths between nodes from a pool of candidate nodes and paths. In addition to the required overlay topology constructed from direct paths between nodes, QoSMap provides path resiliency by constructing alternate one-hop overlay routes via intermediary nodes having paths that meet or exceed the resource constraints. As a case study, we utilized QoSMap to form an overlay for an application requiring constraints on message delay and loss rates. We describe the design of QoSMap and show that it leads to higher quality and more resilient overlays than does a mechanism which addresses only the minimum QoS requirements of the application.