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  • 1. Ghoshal, G.
    et al.
    Holme, Petter
    Attractiveness and activity in Internet communities2006In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 364, p. 603-609Article in journal (Refereed)
    Abstract [en]

    Data sets of online communication often take the form of contact sequences-ordered lists contacts (where a contact is defined as a triple of a sender, a recipient and a time). We propose measures of attractiveness and activity for such data sets and analyze these quantities for anonymized contact sequences from an Internet dating community. For this data set the attractiveness and activity measures show broad power-law-like distributions. Our attractiveness and activity measures are more strongly correlated in the real-world data than in our reference model. Effects that indirectly can make active users more attractive are discussed.

  • 2. Grönlund, A
    et al.
    Holme, Petter
    A network-based threshold model for the spreading of fads in society and markets2005In: Advances in Complex Systems, ISSN 0219-5259, Vol. 8, no 2-3, p. 261-273Article in journal (Refereed)
    Abstract [en]

    We investigate the behavior of a threshold model for the spreading of fads and similar phenomena in society. The model gives the fad dynamics and is intended to be confined to an underlying network structure. We investigate the whole parameter space of the fad dynamics on three types of network models. The dynamics we discover is rich and highly dependent on the underlying network structure. For some range of the parameter space, for all types of substrate networks, there are a great variety of sizes and life-lengths of the fads - what one sees in real-world social and economical systems.

  • 3. Grönlund, Andreas
    et al.
    Holme, Petter
    Networking the seceder model: Group formation in social and economic systems2004In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 70, no 3, p. 036108-Article in journal (Refereed)
    Abstract [en]

    The seceder model illustrates how the desire to be different from the average can lead to formation of groups in a population. We turn the original, agent based, seceder model into a model of network evolution. We find that the structural characteristics of our model closely match empirical social networks. Statistics for the dynamics of group formation are also given. Extensions of the model to networks of companies are also discussed.

  • 4. Grönlund, Andreas
    et al.
    Holme, Petter
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Minnhagen, Petter
    Dynamic scaling regimes of collective decision making2008In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 81, no 2, p. 28003-Article in journal (Refereed)
    Abstract [en]

    We investigate a social system of agents faced with a binary choice. We assume there is a correct, or beneficial, outcome of this choice. Furthermore, we assume agents are influenced by others in making their decision, and that the agents can obtain information that may guide them towards making a correct decision. The dynamic model we propose is of nonequilibrium type, converging to a final decision. We run it on random graphs and scale-free networks. On random graphs, we find two distinct regions in terms of the finalizing time-the time until all agents have finalized their decisions. On scale-free networks, on the other hand, there do not seem to be such distinct scaling regions.

  • 5. Holme, Petter
    Congestion and centrality in traffic flow on complex networks2003In: Advances in Complex Systems, ISSN 0219-5259, Vol. 6, no 2, p. 163-176Article in journal (Refereed)
    Abstract [en]

    The central points of communication network flow have often been identified using graph theoretical centrality measures. In real networks, the state of traffic density arises from an interplay between the dynamics of the flow and the underlying network structure. In this work we investigate the relationship between centrality measures and the density of traffic for some simple particle hopping models on networks with emerging scale-free degree distributions. We also study how the speed of the dynamics are affected by the underlying network structure. Among other conclusions, we find that, even at low traffic densities, the dynamical measure of traffic density (the occupation ratio) has a non-trivial dependence on the static centrality (quantified by "betweenness centrality"), where non-central vertices get a comparatively large portion of the traffic.

  • 6. Holme, Petter
    Core-periphery organization of complex networks2005In: Physical Review E, ISSN 1539-3755, Vol. 72, no 4Article in journal (Refereed)
    Abstract [en]

    Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy. We measure this coefficient for a number of real-world and model networks and find that different classes of networks have their characteristic values. Among other things we conclude that geographically embedded transportation networks have a strong core-periphery structure. We proceed to study radial statistics of the core, i.e., properties of the n neighborhoods of the core vertices for increasing n. We find that almost all networks have unexpectedly many edges within n neighborhoods at a certain distance from the core suggesting an effective radius for nontrivial network processes.

  • 7. Holme, Petter
    Detecting degree symmetries in networks2006In: Physical Review E, ISSN 1539-3755, Vol. 74, no 3Article in journal (Refereed)
    Abstract [en]

    The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry-the property that many paths going out from a vertex have overlapping degree sequences. These measures are evaluated on artificial and real networks. Specifically we consider vertices in the human metabolic network. We also measure the average degree-symmetry coefficient for different classes of real-world network. We find that most studied examples are weakly positively degree symmetric. The exceptions are an airport network (having a negative degree-symmetry coefficient) and one-mode projections of social affiliation networks that are rather strongly degree symmetric.

  • 8. Holme, Petter
    Edge overload breakdown in evolving networks2002In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 66, no 3, p. 036119-Article in journal (Refereed)
    Abstract [en]

    We investigate growing networks based on Barabasi and Albert's algorithm for generating scale-free networks, but with edges sensitive to overload breakdown. The load is defined through edge betweenness centrality. We focus on the situation where the average number of connections per vertex is, like the number of vertices, linearly increasing in time. After an initial stage of growth, the network undergoes avalanching breakdowns to a fragmented state from which it never recovers. This breakdown is much less violent if the growth is by random rather than by preferential attachment (as defines the Barabasi and Albert model). We briefly discuss the case where the average number of connections per vertex is constant. In this case no breakdown avalanches occur. Implications to the growth of real-world communication networks are discussed.

  • 9. Holme, Petter
    Efficient local strategies for vaccination and network attack2004In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 68, no 6, p. 908-914Article in journal (Refereed)
    Abstract [en]

    We study how a fraction of a population should be vaccinated to most efficiently stop epidemics. Our starting point is that only local information-about the neighborhood of specific vertices-is usable in practice. For this reason we consider only local vaccination strategies. The efficiency of the vaccination strategies is investigated with both static and dynamic measures. We test the strategies on real-world networks and model networks with real-world characteristics. Among other things, we find that the most efficient strategy for many real-world situations is to iteratively vaccinate the neighbor of the previous vaccinee that has the most links out of the neighborhood.

  • 10. Holme, Petter
    Local symmetries in complex networks2007In: Journal of the Korean Physical Society, ISSN 0374-4884, E-ISSN 1976-8524, Vol. 50, no 1, p. 300-303Article in journal (Refereed)
    Abstract [en]

    Symmetry-invariance to certain operators-is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent in many complex networks, we consider measures that are continuous rather than dichotomous. The main operator we suggest is permutations of paths of a certain length leading out from a vertex. If these paths are more similar (in some sense) than expected, the vertex is a local center of symmetry in the network. We discuss different precise definitions based on this idea and give examples how different symmetry coefficients can be applied to protein interaction networks.

  • 11.
    Holme, Petter
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Model validation of simple-graph representations of metabolism2009In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 6, no 40, p. 1027-1034Article in journal (Refereed)
    Abstract [en]

    The large-scale properties of chemical reaction systems, such as metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information, lists of chemical reactions, available in databases. Even for the simplest type of graph representation, this reduction can be done in several ways. We investigate different simple network representations by testing how well they encode information about one biologically important network structure-network modularity (the propensity for edges to be clustered into dense groups that are sparsely connected between each other). To achieve this goal, we design a model of reaction systems where network modularity can be controlled and measure how well the reduction to simple graphs captures the modular structure of the model reaction system. We find that the network types that best capture the modular structure of the reaction system are substrate-product networks (where substrates are linked to products of a reaction) and substance networks (with edges between all substances participating in a reaction). Furthermore, we argue that the proposed model for reaction systems with tunable clustering is a general framework for studies of how reaction systems are affected by modularity. To this end, we investigate statistical properties of the model and find, among other things, that it recreates correlations between degree and mass of the molecules.

  • 12. Holme, Petter
    Network dynamics of ongoing social relationships2003In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 64, no 3, p. 427-433Article in journal (Refereed)
    Abstract [en]

    Many recent large-scale studies of interaction networks have focused on networks of accumulated contacts. In this letter we explore social networks of ongoing relationships with an emphasis on dynamical aspects. We find a distribution of response times (times between consecutive contacts of different direction between two actors) that has a power law shape over a large range. We also argue that the distribution of relationship duration (the time between the first and last contacts between actors) is exponentially decaying. Methods to reanalyze the data to compensate for the finite sampling time are proposed. We find that the degree distribution for networks of ongoing contacts fits better to a power law than the degree distribution of the network of accumulated contacts do. We see that the clustering and assortative mixing coefficients are of the same order for networks of ongoing and accumulated contacts, and that the structural fluctuations of the former are rather large.

  • 13. Holme, Petter
    Network reachability of real-world contact sequences2005In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 71, no 4Article in journal (Refereed)
    Abstract [en]

    We use real-world contact sequences, time-ordered lists of contacts from one person to another, to study how fast information or disease can spread across network of contacts. Specifically we measure the reachability time-the average shortest time for a series of contacts to spread information between a reachable pair of vertices (a pair where a chain of contacts exists leading from one person to the other)-and the reachability ratio-the fraction of reachable vertex pairs. These measures are studied using conditional uniform graph tests. We conclude, among other things, that the network reachability depends much on a core where the path lengths are short and communication frequent, that clustering of the contacts of an edge in time tends to decrease the reachability, and that the order of the contacts really does make sense for dynamical spreading processes.

  • 14. Holme, Petter
    Scale-free networks with a large- to hypersmall-world transition2007In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 377, no 1, p. 315-322Article in journal (Refereed)
    Abstract [en]

    Recently there has been a tremendous interest in models of networks with a power-law distribution of degree-so-called scale-free networks. It has been observed that such networks, normally, have extremely short path-lengths, scaling logarithmically or slower with system size. As an exotic and counterintuitive example we propose a simple stochastic model capable of generating scale-free networks with linearly scaling distances. Furthermore, by tuning a parameter the model undergoes a phase transition to a regime with extremely short average distances, apparently slower than log log N (which we call a hypersmall-world regime). We characterize the degree degree correlation and clustering properties of this class of networks.

  • 15.
    Holme, Petter
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Signatures of Currency Vertices2009In: Journal of the Physical Society of Japan, ISSN 0031-9015, E-ISSN 1347-4073, Vol. 78, no 3, p. 034801-Article in journal (Refereed)
    Abstract [en]

    Many real-world networks have broad degree distributions. For some systems, this means that the functional of the vertices is also broadly distributed, in other cases the vertices are equally significant, but in different ways. One example of the latter case is metabolic networks, where the high-degree vertices the currency metabolites-supply the molecular groups to the low-degree metabolites, and the latter are responsible for the higher-order biological function, Of Vital importance to the organism. In this paper, we propose a generalization of currency metabolites to currency vertices. We investigate the network structural characteristics of such systems, both in model networks and in sonic empirical systems. fit addition to metabolic networks, we find that a network of music collaborations and a network of e-mail exchange could be described by a division of the vertices into currency vertices and others.

  • 16. Holme, Petter
    et al.
    Edling, C. R.
    Liljeros, F.
    Structure and time evolution of an Internet dating community2004In: Social Networks, ISSN 0378-8733, E-ISSN 1879-2111, Vol. 26, no 2, p. 155-174Article in journal (Refereed)
    Abstract [en]

    We present statistics for the structure and time evolution of a network constructed from user activity in an Internet community. The vastness and precise time resolution of an Internet community offers unique possibilities to monitor social network formation and dynamics. Time evolution of well-known quantities, such as clustering, mixing (degree-degree correlations), average geodesic length, degree, and reciprocity is studied. In contrast to earlier analyses of scientific collaboration networks, mixing by degree between vertices is found to be disassortative. Furthermore, both the evolutionary trajectories of the average geodesic length and of the clustering coefficients are found to have minima.

  • 17. Holme, Petter
    et al.
    Ghoshal, G.
    Dynamics of networking agents competing for high centrality and low degree2006In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 96, no 9Article in journal (Refereed)
    Abstract [en]

    We model a system of networking agents that seek to optimize their centrality in the network while keeping their cost, the number of connections they are participating in, low. Unlike other game-theory based models for network evolution, the success of the agents is related only to their position in the network. The agents use strategies based on local information to improve their chance of success. Both the evolution of strategies and network structure are investigated. We find a dramatic time evolution with cascades of strategy change accompanied by a change in network structure. On average the network self-organizes to a state close to the transition between a fragmented state and a state with a giant component. Furthermore, with increasing system size both the average degree and the level of fragmentation decreases.

  • 18. Holme, Petter
    et al.
    Grönlund, Andreas
    Modelling the dynamics of youth subcultures2005In: JASSS: Journal of Artificial Societies and Social Simulation, ISSN 1460-7425, E-ISSN 1460-7425, Vol. 8, no 3Article in journal (Refereed)
    Abstract [en]

    What are the dynamics behind youth subcultures such as punk, hippie, or hip-hop cultures? How does the global dynamics of these subcultures relate to the individual's search for a personal identity? We propose a simple dynamical model to address these questions and find that only a few assumptions of the individual's behaviour are necessary to regenerate known features of youth culture.

  • 19. Holme, Petter
    et al.
    Huss, M.
    Role-similarity based functional prediction in networked systems: application to the yeast proteome2005In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 2, no 4, p. 327-333Article in journal (Refereed)
    Abstract [en]

    We propose a general method to predict functions of vertices where (i) the wiring of the network is somehow related to the vertex functionality and (ii) a fraction of the vertices are functionally classified. The method is influenced by role-similarity measures of social network analysis. The two versions of our prediction scheme axe tested on model networks where the functions of the vertices are designed to match their network surroundings. We also apply these methods to the proteome of the yeast Saccharomyces cerevisiae and find the results compatible with more specialized methods.

  • 20.
    Holme, Petter
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Huss, Mikael
    Comment on "Regularizing capacity of metabolic networks"2008Article in journal (Refereed)
    Abstract [en]

    In a recent paper, Marr, Muller-Linow, and Hutt [Phys. Rev. E 75, 041917 (2007)] investigate an artificial dynamic system on metabolic networks. They find a less complex time evolution of this dynamic system in real networks, compared to networks of null models. The authors argue that this suggests that metabolic network structure is a major factor behind the stability of biochemical steady states. We reanalyze the same kind of data using a dynamic system modeling actual reaction kinetics. The conclusions about stability, from our analysis, are inconsistent with those of Marr We argue that this issue calls for a more detailed type of modeling.

  • 21.
    Holme, Petter
    et al.
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Huss, Mikael
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Jeong, H. W.
    Subnetwork hierarchies of biochemical pathways2003In: Bioinformatics, ISSN 1367-4803, E-ISSN 1367-4811, Vol. 19, no 4, p. 532-538Article in journal (Refereed)
    Abstract [en]

    Motivation: The vastness and complexity of the biochemical networks that have been mapped out by modern genomics calls for decomposition into subnetworks. Such networks can have inherent non-local features that require the global structure to be taken into account in the decomposition procedure. Furthermore, basic questions such as to what extent the network (graph theoretically) can be said to be built by distinct subnetworks are little studied. Results: We present a method to decompose biochemical networks into subnetworks based on the global geometry of the network. This method enables us to analyze the full hierarchical organization of biochemical networks and is applied to 43 organisms from the WIT database. Two types of biochemical networks are considered: metabolic networks and whole-cellular networks (also including for example information processes). Conceptual and quantitative ways of describing the hierarchical ordering are discussed. The general picture of the metabolic networks arising from our study is that of a few core-clusters centred around the most highly connected substances enclosed by other substances in outer shells, and a few other well-defined subnetworks.

  • 22.
    Holme, Petter
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Karlin, Josh
    Forrest, Stephanie
    An integrated model of traffic, geography and economy in the internet2008In: Computer communication review, ISSN 0146-4833, E-ISSN 1943-5819, Vol. 38, no 3, p. 7-15Article in journal (Refereed)
    Abstract [en]

    Modeling Internet growth is important both for understanding the current network and to predict and improve its future. To date, Internet models have typically attempted to explain a subset of the following characteristics: network structure, traffic flow, geography, and economy. In this paper we present a discrete, agent-based model, that integrates all of them. We show that the model generates networks with topologies, dynamics, and more speculatively spatial distributions that are similar to the Internet.

  • 23. Holme, Petter
    et al.
    Karlin, Josh
    Forrest, Stephanie
    Radial structure of the Internet2007In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 463, no 2081, p. 1231-1246Article in journal (Refereed)
    Abstract [en]

    The structure of the Internet at the autonomous system (AS) level has been studied by the physics, mathematics and computer science communities. We extend this work to include features of the core and the periphery, taking a radial perspective on AS network structure. New methods for plotting AS data are described, and they are used to analyse datasets that have been extended to contain edges missing from earlier collections. The average distance from one vertex to the rest of the network is used as the baseline metric for investigating radial structure. Common vertex-specific quantities are plotted against this metric to reveal distinctive characteristics of central and peripheral vertices. Two datasets are analysed using these measures as well as two common generative models (Barabasi-Albert and Inet) We find a clear distinction between the highly connected core and a sparse periphery. We also find that the periphery has a more complex structure than that predicted by degree distribution or the two generative models.

  • 24. Holme, Petter
    et al.
    Kim, Beom Jun
    Growing scale-free networks with tunable clustering2002In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 65, no 2, p. 026107-Article in journal (Refereed)
    Abstract [en]

    We extend the standard scale-free network model to include a "triad formation step." We analyze the Geometric properties of networks Generated by this algorithm both analytically and by numerical calculations, and find that our model possesses the same characteristics as the standard scale-free networks such as the power-law degree distribution and the small average geodesic length, but with the high clustering at the same time. In our model, the clustering coefficient is also shown to be tunable simply by changing a control parameter-the average number of triad formation trials per time step.

  • 25. Holme, Petter
    et al.
    Kim, Beom Jun
    Vertex overload breakdown in evolving networks2002In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 65, no 6, p. 066109-Article in journal (Refereed)
    Abstract [en]

    We study evolving networks based on the Barabasi-Albert scale-free network model with vertices sensitive to overload breakdown. The load of a vertex is defined as the betweenness centrality of the vertex. Two cases of load limitation are considered, corresponding to the fact that the average number of connections per vertex is increasing with the network's size ("extrinsic communication activity"), or that it is constant ("intrinsic communication activity"). Avalanchelike breakdowns for both load limitations are observed. In order to avoid such avalanches we argue that the capacity of the vertices has to grow with the size of the system. An interesting irregular dynamics of the formation of the giant component (for the intrinsic communication activity case) is also studied. Implications on the growth of the Internet are discussed.

  • 26.
    Holme, Petter
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Kim, Beom Jun
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Fodor, Viktoria
    KTH, School of Electrical Engineering (EES), Communication Networks.
    Heterogeneous attachment strategies optimize the topology of dynamic wireless networks2010In: European Physical Journal B: Condensed Matter Physics, ISSN 1434-6028, E-ISSN 1434-6036, Vol. 73, no 4, p. 597-604Article in journal (Refereed)
    Abstract [en]

    In optimizing the topology of wireless networks built of a dynamic set of spatially embedded agents, there are many trade-offs to be dealt with. The network should preferably be as small (in the sense that the average, or maximal, pathlength is short) as possible, it should be robust to failures, not consume too much power, and so on. In this paper, we investigate simple models of how agents can choose their neighbors in such an environment. In our model of attachment, we can tune from one situation where agents prefer to attach to others in closest proximity, to a situation where agents attach to random others regardless of distance (which thus are, on average, further away than the connections to the spatial neighbors). We evaluate this scenario with several performance measures and find that the optimal topologies, for most of the quantities, is obtained for strategies resulting in a mix of most local and a few random connections.

  • 27. Holme, Petter
    et al.
    Kim, Beom Jun
    Minnhagen, P.
    Phase transitions in the two-dimensional random gauge XY model2003In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 67, no 10Article in journal (Refereed)
    Abstract [en]

    The two-dimensional random gauge XY model, where the quenched random variables are magnetic bond angles uniformly distributed within [(-)rpi,rpi](0less than or equal torless than or equal to1), is studied via Monte Carlo simulations. We investigate the phase diagram in the plane of the temperature T and the disorder strength r and infer, in contrast to a prevailing conclusion in many earlier studies, that the system is superconducting at any disorder strength r for sufficiently low T. It is also argued that the superconducting to normal transition has different nature at weak disorder and strong disorder: termed Kosterlitz-Thouless (KT) type and non-KT type, respectively. The results are compared to earlier works.

  • 28. Holme, Petter
    et al.
    Kim, Beom Jun
    Yoon, C. N.
    Han, S. K.
    Attack vulnerability of complex networks2002In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 65, no 5, p. 056109-Article in journal (Refereed)
    Abstract [en]

    We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and the network performance is quantitatively measured by the average inverse geodesic length and the size of the largest connected subgraph. For each case of attacks on vertices and edges, four different attacking strategies are used: removals by the descending order of the degree and the betweenness centrality, calculated for either the initial network or the current network during the removal procedure. It is found that the removals by the recalculated degrees and betweenness centralities are often more harmful than the attack strategies based on the initial network, suggesting that the network structure changes as important vertices or edges are removed. Furthermore, the correlation between the betweenness centrality and the degree in complex networks is studied.

  • 29. Holme, Petter
    et al.
    Liljeros, Fredrik
    Edling, Christofer R.
    Kim, Beom Jun
    Network bipartivity2003In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 68, no 5, p. 056107-Article in journal (Refereed)
    Abstract [en]

    Systems with two types of agents with a preference for heterophilous interaction produce networks that are more or less close to bipartite. We propose two measures quantifying the notion of bipartivity. The two measures-one well known and natural, but computationally intractable, and the other computationally less complex, but also less intuitive-are examined on model networks that continuously interpolate between bipartite graphs and graphs with many odd circuits. We find that the bipartivity measures increase as we tune the control parameters of the test networks to intuitively increase the bipartivity, and thus conclude that the measures are quite relevant. We also measure and discuss the values of our bipartivity measures for empirical social networks (constructed from professional collaborations, Internet communities, and field surveys). Here we find, as expected, that networks arising from romantic online interaction have high, and professional collaboration networks have low, bipartivity values. In some other cases, probably due to low average degree of the network, the bipartivity measures cannot distinguish between romantic and friendship oriented interaction.

  • 30. Holme, Petter
    et al.
    Newman, M. E. J.
    Nonequilibrium phase transition in the coevolution of networks and opinions2006In: Physical Review E, ISSN 1539-3755, Vol. 74, no 5Article in journal (Refereed)
    Abstract [en]

    Models of the convergence of opinion in social systems have been the subject of considerable recent attention in the physics literature. These models divide into two classes, those in which individuals form their beliefs based on the opinions of their neighbors in a social network of personal acquaintances, and those in which, conversely, network connections form between individuals of similar beliefs. While both of these processes can give rise to realistic levels of agreement between acquaintances, practical experience suggests that opinion formation in the real world is not a result of one process or the other, but a combination of the two. Here we present a simple model of this combination, with a single parameter controlling the balance of the two processes. We find that the model undergoes a continuous phase transition as this parameter is varied, from a regime in which opinions are arbitrarily diverse to one in which most individuals hold the same opinion.

  • 31. Holme, Petter
    et al.
    Olsson, P.
    A zero-temperature study of vortex mobility in two-dimensional vortex glass models2002In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 60, no 3, p. 439-445Article in journal (Refereed)
    Abstract [en]

    Three different vortex glass models are studied by examining the energy barrier against vortex motion cross the system. In the two-dimensional gauge glass this energy barrier is found to increase logarithmically with system size which opens up for the existence of low-temperature phase with zero resistivity. Associated with the large-energy barriers is breaking of ergodicity which explains why the well-established results from equilibrium studies could fail. The behavior of the more realistic random pinning model is however different with decreasing energy barriers and no finite critical temperature.

  • 32. Holme, Petter
    et al.
    Park, Min
    Kim, Jun
    Edling, Christofer R.
    Korean university life in a network perspective: Dynamics of a large affiliation network2007In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 373, p. 821-830Article in journal (Refereed)
    Abstract [en]

    We investigate course registration data of 18 semesters at a Korean University to portray the time evolution of students' positions in the network of fellow students. Apart from being a study of the social positions of students, the present work is also an example of how large-scale, time resolved, affiliation networks can be analyzed. For example, we discuss the proper definitions of weights, and propose a redefined weighted clustering coefficient. Among other things, we find that the students enter the network at the center and are gradually diffusing towards the periphery. On the other hand, the ties to the classmates of the first semester will, on average, become stronger as time progresses. (c) 2006 Elsevier B.V. All rights reserved.

  • 33. Holme, Petter
    et al.
    Trusina, A.
    Kim, Beom Jun
    Minnhagen, Petter
    Prisoners' dilemma in real-world acquaintance networks: Spikes and quasiequilibria induced by the interplay between structure and dynamics2003In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 68, no 3, p. 030901-Article in journal (Refereed)
    Abstract [en]

    We study Nowak and May's spatial prisoners' dilemma game driven by mutations (random choices of suboptimal strategies) on empirical social networks. The time evolution of the cooperation level is highly complex containing spikes and steps between quasistable levels. A statistical characterization of the quasistable states and a study of the mechanisms behind the steps are given. We argue that the crucial structural ingredients causing the observed behavior is an inhomogeneous degree distribution and that the connections within vertices of highest degree are rather sparse. Based on these observations we construct model networks with a similar complex time evolution of the cooperation level.

  • 34. Holme, Petter
    et al.
    Zhao, Jing
    Exploring the assortativity-clustering space of a network's degree sequence2007In: Physical Review E, ISSN 1539-3755, Vol. 75, no 4Article in journal (Refereed)
    Abstract [en]

    Nowadays there is a multitude of measures designed to capture different aspects of network structure. To be able to say if a measured value is expected or not, one needs to compare it with a reference model (null model). One frequently used null model is the ensemble of graphs with the same set of degrees as the original network. Here, we argue that this ensemble can give more information about the original network than effective values of network structural quantities. By mapping out this ensemble in the space of some low-level network structure-in our case, those measured by the assortativity and clustering coefficients-one can, for example, study where in the valid region of the parameter space the observed networks are. Such analysis suggests which quantities (or combination of quantities) are actively optimized during the evolution of the network. We use four very different biological networks to exemplify our method. Among other things, we find that high clustering might be a force in the evolution of protein interaction networks. We also find that all four networks are conspicuously robust to both random errors and targeted attacks.

  • 35.
    Huss, Mikael
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Holme, Petter
    Currency and commodity metabolites: their identification and relation to the modularity of metabolic networks2007In: IET Systems Biology, ISSN 1751-8849, Vol. 1, no 5, p. 280-285Article in journal (Refereed)
    Abstract [en]

    The large-scale shape and function of metabolic networks are intriguing topics of systems biology. Such networks are on one hand commonly regarded as modular (i.e. built by a number of relatively independent subsystems), but on the other hand they are robust in a way not necessarily expected of a purely modular system. To address this question, we carefully discuss the partition of metabolic networks into subnetworks. The practice of preprocessing such networks by removing the most abundant substances, 'currency metabolites', is formalized into a network-based algorithm. We study partitions for metabolic networks of many organisms and find cores of currency metabolites and modular peripheries of what we call 'commodity metabolites'. The networks are found to be more modular than random networks but far from perfectly divisible into modules. We argue that cross-modular edges are the key for the robustness of metabolism.

  • 36. Kim, Beom Jun
    et al.
    Hong, H.
    Holme, Petter
    Jeon, G. S.
    Minnhagen, Petter
    Choi, M. Y.
    XY model in small-world networks2001In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 64, no 5, p. 056135-Article in journal (Refereed)
    Abstract [en]

    The phase transition in the XY model on one-dimensional small-world networks is investigated by means of Monte Carlo simulations. It is found that long-range order is present at finite temperatures, even for very small values of the rewiring probability, suggesting a finite-temperature transition for any nonzero rewiring probability. Nature of the phase transition is discussed in comparison with the globally coupled XY model.

  • 37. Kim, Beom Jun
    et al.
    Trusina, A
    Holme, Petter
    Minnhagen, Petter
    Chung, S
    Choi, M.Y.
    Dynamic instabilities induced by asymmetric influence: Prisoners' dilemma game in small-world networks2002In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 66, no 2, p. 021907-Article in journal (Refereed)
    Abstract [en]

    A two-dimensional small-world-type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node, with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium-type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is linked to an imitation of a successful selfish strategy of the influential node. It is also found that while the breakdown of cooperation occurs suddenly, its recovery requires longer time. This recovery time may, depending on the degree of steady state cooperation, either increase or decrease with an increasing number of long-range connections.

  • 38. Leicht, E. A.
    et al.
    Holme, Petter
    Newman, M. E. J.
    Vertex similarity in networks2006In: Physical Review E, ISSN 1539-3755, Vol. 73, no 2Article in journal (Refereed)
    Abstract [en]

    We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads to a self-consistent matrix formulation of similarity that can be evaluated iteratively using only a knowledge of the adjacency matrix of the network. We test our similarity measure on computer-generated networks for which the expected results are known, and on a number of real-world networks.

  • 39. Liljeros, Fredrik
    et al.
    Giesecke, Johan
    Holme, Petter
    The contact network of inpatients in a regional healthcare system. A longitudinal case study2007In: Mathematical Population Studies, ISSN 0889-8480, Vol. 14, no 4, p. 269-284Article in journal (Refereed)
    Abstract [en]

    Contact networks are extracted for 295,108 inpatients over a two-year period from a database used for administering a local public healthcare system that serves 1.8 million individuals in Stockholm county. Structural and dynamic properties of the network that are important for the transmission of contagious diseases are analyzed by methods derived from network epidemiology. The contact networks are found to be very much determined by an extreme (age-independent) variation in the duration of hospital stays and the hospital structure. The structure of contacts between inpatients are found to exhibit structural properties such as a high level of transitivity, assortativity, and variation by number of contacts, which are likely to be of importance for the transmission of less contagious diseases. If these properties are considered when designing prevention programs, the risk and effect of epidemic outbreaks may be decreased.

  • 40. Medvedyeva, Kateryna
    et al.
    Holme, Petter
    Minnhagen, Petter
    Kim, Beom Jun
    Dynamic critical behavior of the XY model in small-world networks2003In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 67, no 3, p. 036118-Article in journal (Refereed)
    Abstract [en]

    The critical behavior of the XY model on small-world network is investigated by means of dynamic Monte Carlo simulations. We use the short-time relaxation scheme, i.e., the critical behavior is studied from the nonequilibrium relaxation to equilibrium. Static and dynamic critical exponents are extracted through the use of the dynamic finite-size scaling analysis. It is concluded that the dynamic universality class at the transition is of the mean-field nature. We also confirm numerically that the value of dynamic critical exponent is independent of the rewiring probability P for Pgreater than or similar to0.03.

  • 41. Nonaka, Etsuko
    et al.
    Holme, Petter
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Agent-based model approach to optimal foraging in heterogeneous landscapes: effects of patch clumpiness2007In: Ecography, ISSN 0906-7590, E-ISSN 1600-0587, Vol. 30, no 6, p. 777-788Article in journal (Refereed)
    Abstract [en]

    Optimal foraging theory concerns animal behavior in landscapes where food is concentrated in patches. The efficiency of foraging is an effect of both the animal behavior and the geometry of the landscape; furthermore, the landscape is itself affected by the foraging of animals. We investigated the effect of landscape heterogeneity on the efficiency of an optimal forager. The particular aspect of heterogeneity we considered was clumpiness- the degree to which food resource patches are clustered together. The starting point for our study was the framework of the Mean Value Theorem (MVT) by Charnov. Since MVT is not spatially explicit, and thus not apt to investigate effects of clumpiness, we built an agent-based (or individual-based) model for animal movement in discrete landscapes extending the MVT. We also constructed a model for generating landscapes where the clumpiness of patches can be easily controlled, or tuned, by an input parameter. We evaluated the agent based model by comparing the results with what the MTV would give, i.e. if the spatial effects were removed. The MVT matched the simulations best on landscapes with random patch configuration and high food recovery rates. As for our main question about the effects of clumpiness, we found that, when landscapes were highly productive (rapid food replenishment), foraging efficiency was greatest in clumped landscapes. In less productive landscapes, however, foraging efficiency was lowest in landscapes with a clumped patch distribution.

  • 42. Olsson, P.
    et al.
    Holme, Petter
    Comment on structure and phase transition of Josephson vortices in anisotropic High-T-c superconductors2000In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 85, no 12, p. 2651-2651Article in journal (Refereed)
  • 43. Olsson, P.
    et al.
    Holme, Petter
    Transition in the two-dimensional step model: A Kosterlitz-Thouless transition in disguise2001In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 6305, no 5Article in journal (Refereed)
    Abstract [en]

    Evidence for a Kosterlitz-Thouless transition in the two-dimensional (2D) step model is obtained from Monte Carlo determinations of the helicity modulus. It is argued that the free energy of a single vortex at the center of the system depends logarithmically on the system size in spite of the fact that the spin interaction is not harmonic for small differences in the spin angles. We conclude that this is the reason for the Kosterlitz-Thouless transition in the 2D step model and that the harmonic spin interaction not is a necessary requirement.

  • 44. Zhou, T.
    et al.
    Kiet, H. A. T.
    Kim, Beom Jun
    Wang, B. H.
    Holme, Petter
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Role of activity in human dynamics2008In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 82, no 2Article in journal (Refereed)
    Abstract [en]

    The human society is a very complex system; still, there are several non-trivial, features. One type of them is the presence of power-law-distributed quantities in temporal statistics. In this letter, we focus on the origin of power laws in rating of movies. We present a systematic empirical exploration of the time between two consecutive ratings of movies ( the interevent time). At an aggregate level, we find a monotonous relation between the activity of individuals and the power law exponent of the interevent time distribution. At an individual level, we observe a heavy-tailed distribution for each user, as well as a negative correlation between the activity and the width of the distribution. We support these findings by a similar data set from mobile phone text-message communication. Our results demonstrate a significant role of the activity of individuals on the society-level patterns of human behavior. We believe this is a common character in the interest-driven human dynamics, corresponding to (but different from) the universality classes of task-driven dynamics.

1 - 44 of 44
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