arXiv subjects

Petter Holme

Publications and source records attributed to Petter Holme.

At least 127 records · Page 7Linked to original sources

arXiv2009

Multiscaling in the YX model of networks

We investigate a Hamiltonian model of networks. The model is a mirror formulation of the XY model (hence the name) -- instead letting the XY spins vary, keeping the coupling topology static, we keep the spins conserved and sample different underlying networks. Our numerical simulations show complex scaling behaviors, but no finite-temperature critical behavior. The ground state and low-order excitations for sparse, finite graphs is a fragmented set of isolated network clusters. Configurations of higher energy are typically more connected. The connected networks of lowest energy are stretched out giving the network large average distances. For the finite sizes we investigate there are three regions -- a low-energy regime of fragmented networks, and intermediate regime of stretched-out networks, and a high-energy regime of compact, disordered topologies. Scaling up the system size, the borders between these regimes approach zero temperature algebraically, but different network structural quantities approach their T=0-values with different exponents.

physics.comp-ph↗

arXiv2009

Heterogeneous attachment strategies optimize the topology of dynamic wireless networks

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 distance is ignored (and thus attachments can be made to agents further away). 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.

cs.NI↗

arXiv2008

Signatures of currency vertices

Many real-world networks have broad degree distributions. For some systems, this means that the functional significance 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 some empirical systems. In 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.

physics.soc-ph↗

arXiv2008

Model validation of simple-graph representations of metabolism

The large-scale properties of chemical reaction systems, such as the 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 cluster into dense groups that are sparsely connected between each other). To reach this goal, we design a model of reaction-systems where network modularity can be controlled and measure how well the reduction to simple graphs capture 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 recreate correlations between degree and mass of the molecules.

q-bio.MN↗

arXiv2008

Substance graphs are optimal simple-graph representations of metabolism

One approach to studying the system-wide organization of biochemistry is to use statistical graph theory. Even in such a heavily simplified method, which disregards most of the dynamic aspects of biochemistry, one is faced with fundamental questions, such as how the chemical reaction systems should be reduced to a graph retaining as much functional information as possible from the original reaction system. In such graph representations, should the edges go between substrates and products, or substrates and substrates, or both? Should vertices represent substances or reactions? Different definitions encode different information about the reaction system. In this paper we evaluate four different graph representations of metabolism, applied to data from different organisms and databases. The graph representations are evaluated by comparing the overlap between clusters (network modules) and annotated functions, and also by comparing the set of identified currency metabolites with those that other authors have identified using qualitative biological arguments. We find that a "substance network," where all metabolites participating in a reaction are connected, is relatively better than others, evaluated both with respect to the functional overlap between modules and functions and to the number and identity of identified currency metabolites.

q-bio.MN↗

arXiv2008

The diplomat's dilemma: Maximal power for minimal effort in social networks

Closeness is a global measure of centrality in networks, and a proxy for how influential actors are in social networks. In most network models, and many empirical networks, closeness is strongly correlated with degree. However, in social networks there is a cost of maintaining social ties. This leads to a situation (that can occur in the professional social networks of executives, lobbyists, diplomats and so on) where agents have the conflicting objectives of aiming for centrality while simultaneously keeping the degree low. We investigate this situation in an adaptive network-evolution model where agents optimize their positions in the network following individual strategies, and using only local information. The strategies are also optimized, based on the success of the agent and its neighbors. We measure and describe the time evolution of the network and the agents' strategies.

physics.soc-ph↗

arXiv2008

An integrated model of traffic, geography and economy in the Internet

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.

cs.NI↗

arXiv2008

Role of Activity in Human Dynamics

The human society is a very complex system; still, there are several non-trivial, general 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.

physics.soc-ph↗

arXiv2008

Comment on "Regularizing capacity of metabolic networks"

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 reference 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 et al. We argue that this issue calls for a more detailed type of modeling.

q-bio.MN↗

arXiv2007

Dynamic scaling regimes of collective decision making

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 does not seem to be any such distinct scaling regions.

q-bio.PE↗

arXiv2007

Efficiency of navigation in indexed networks

We investigate efficient methods for packets to navigate in complex networks. The packets are assumed to have memory, but no previous knowledge of the graph. We assume the graph to be indexed, i.e. every vertex is associated with a number (accessible to the packets) between one and the size of the graph. We test different schemes to assign indices and utilize them in packet navigation. Four different network models with very different topological characteristics are used for testing the schemes. We find that one scheme outperform the others, and has an efficiency close to the theoretical optimum. We discuss the use of indexed-graph navigation in peer-to-peer networking and other distributed information systems.

physics.comp-ph↗

arXiv2006

Scale-free networks with a large- to hypersmall-world transition

Recently there have 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 en exotic and unintuitive 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.

cond-mat.dis-nn↗

arXiv2006

Exploring the assortativity-clustering space of a network's degree sequence

Nowadays there is a multitude of measures designed to capture different aspects of network structure. To be able to say if the structure of certain network is expected or not, one needs 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. In this paper we argue that this ensemble can be more than just a null model -- it also carries information about the original network and factors that affect its evolution. 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 how close to the valid region of the parameter space the observed networks are. Such analysis suggests which 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.

q-bio.OT↗

arXiv2006

Local symmetries in complex networks

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 the 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 networks. We discuss different precise definitions based on this idea and give examples how different symmetry coefficients can be applied to protein interaction networks.

cond-mat.dis-nn↗

arXiv2006

Radial Structure of the Internet

The structure of the Internet at the Autonomous System (AS) level has been studied by both the Physics 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 analyze data sets that have been extended to contain edges missing from earlier collections. In particular, 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 data sets are analyzed 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.

cs.NI↗

arXiv2006

Detecting degree symmetries in networks

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.

physics.data-an↗

arXiv2006

Currency and commodity metabolites: Their identification and relation to the modularity of metabolic networks

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 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 substrates, "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.

q-bio.MN↗

arXiv2006

Nonequilibrium phase transition in the coevolution of networks and opinions

Models of the convergence of opinion in social systems have been the subject of a considerable amount of 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. We characterize the static and dynamical properties of this transition.

physics.soc-ph↗