336,942 research outputs found
Evolution of cooperation on dynamical graphs
There are two key characteristic of animal and human societies: (1) degree heterogeneity, meaning that not all individual have the same number of associates; and (2) the interaction topology is not static, i.e. either individuals interact with different set of individuals at different times of their life, or at least they have different associations than their parents. Earlier works have shown that population structure is one of the mechanisms promoting cooperation. However, most studies had assumed that the interaction network can be described by a regular graph (homogeneous degree distribution). Recently there are an increasing number of studies employing degree heterogeneous graphs to model interaction topology. But mostly the interaction topology was assumed to be static. Here we investigate the fixation probability of the cooperator strategy in the prisoner’s dilemma, when interaction network is a random regular graph, a random graph or a scale-free graph and the interaction network is allowed to change.
We show that the fixation probability of the cooperator strategy is lower when the interaction topology is described by a dynamical graph compared to a static graph. Even a limited network dynamics significantly decreases the fixation probability of cooperation, an effect that is mitigated stronger by degree heterogeneous networks topology than by a degree homogeneous one. We have also found that from the considered graph topologies the decrease of fixation probabilities due to graph dynamics is the lowest on scale-free graphs
Limits on Relief through Constrained Exchange on Random Graphs
Agents are represented by nodes on a random graph (e.g., small world or
truncated power law). Each agent is endowed with a zero-mean random value that
may be either positive or negative. All agents attempt to find relief, i.e., to
reduce the magnitude of that initial value, to zero if possible, through
exchanges. The exchange occurs only between agents that are linked, a
constraint that turns out to dominate the results. The exchange process
continues until a Pareto equilibrium is achieved. Only 40%-90% of the agents
achieved relief on small world graphs with mean degree between 2 and 40. Even
fewer agents achieved relief on scale-free like graphs with a truncated power
law degree distribution. The rate at which relief grew with increasing degree
was slow, only at most logarithmic for all of the graphs considered; viewed in
reverse, relief is resilient to the removal of links.Comment: 8 pages, 2 figures, 22 references Changes include name change for
Lory A. Ellebracht (formerly Cooperstock, e-mail address stays the same),
elimination of contractions and additional references. We also note that our
results are less surprising in view of other work now cite
Traffic on complex networks: Towards understanding global statistical properties from microscopic density fluctuations
We study the microscopic time fluctuations of traffic load and the global statistical properties of a dense traffic of particles on scale-free cyclic graphs. For a wide range of driving rates R the traffic is stationary and the load time series exhibits antipersistence due to the regulatory role of the superstructure associated with two hub nodes in the network. We discuss how the superstructure affects the functioning of the network at high traffic density and at the jamming threshold. The degree of correlations systematically decreases with increasing traffic density and eventually disappears when approaching a jamming density Rc. Already before jamming we observe qualitative changes in the global network-load distributions and the particle queuing times. These changes are related to the occurrence of temporary crises in which the network-load increases dramatically, and then slowly falls back to a value characterizing free flow
Topology regulates pattern formation capacity of binary cellular automata on graphs
We study the effect of topology variation on the dynamic behavior of a system
with local update rules. We implement one-dimensional binary cellular automata
on graphs with various topologies by formulating two sets of degree-dependent
rules, each containing a single parameter. We observe that changes in graph
topology induce transitions between different dynamic domains (Wolfram classes)
without a formal change in the update rule. Along with topological variations,
we study the pattern formation capacities of regular, random, small-world and
scale-free graphs. Pattern formation capacity is quantified in terms of two
entropy measures, which for standard cellular automata allow a qualitative
distinction between the four Wolfram classes. A mean-field model explains the
dynamic behavior of random graphs. Implications for our understanding of
information transport through complex, network-based systems are discussed.Comment: 16 text pages, 13 figures. To be published in Physica
Unimodular lattice triangulations as small-world and scale-free random graphs
Real-world networks, e.g. the social relations or world-wide-web graphs,
exhibit both small-world and scale-free behaviour. We interpret lattice
triangulations as planar graphs by identifying triangulation vertices with
graph nodes and one-dimensional simplices with edges. Since these
triangulations are ergodic with respect to a certain Pachner flip, applying
different Monte-Carlo simulations enables us to calculate average properties of
random triangulations, as well as canonical ensemble averages using an energy
functional that is approximately the variance of the degree distribution. All
considered triangulations have clustering coefficients comparable with real
world graphs, for the canonical ensemble there are inverse temperatures with
small shortest path length independent of system size. Tuning the inverse
temperature to a quasi-critical value leads to an indication of scale-free
behaviour for degrees . Using triangulations as a random graph model
can improve the understanding of real-world networks, especially if the actual
distance of the embedded nodes becomes important.Comment: 17 pages, 6 figures, will appear in New J. Phy
Exploring networks with traceroute-like probes: theory and simulations
Mapping the Internet generally consists in sampling the network from a
limited set of sources by using traceroute-like probes. This methodology, akin
to the merging of different spanning trees to a set of destination, has been
argued to introduce uncontrolled sampling biases that might produce statistical
properties of the sampled graph which sharply differ from the original ones. In
this paper we explore these biases and provide a statistical analysis of their
origin. We derive an analytical approximation for the probability of edge and
vertex detection that exploits the role of the number of sources and targets
and allows us to relate the global topological properties of the underlying
network with the statistical accuracy of the sampled graph. In particular, we
find that the edge and vertex detection probability depends on the betweenness
centrality of each element. This allows us to show that shortest path routed
sampling provides a better characterization of underlying graphs with broad
distributions of connectivity. We complement the analytical discussion with a
throughout numerical investigation of simulated mapping strategies in network
models with different topologies. We show that sampled graphs provide a fair
qualitative characterization of the statistical properties of the original
networks in a fair range of different strategies and exploration parameters.
Moreover, we characterize the level of redundancy and completeness of the
exploration process as a function of the topological properties of the network.
Finally, we study numerically how the fraction of vertices and edges discovered
in the sampled graph depends on the particular deployements of probing sources.
The results might hint the steps toward more efficient mapping strategies.Comment: This paper is related to cond-mat/0406404, with explorations of
different networks and complementary discussion
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