84,048 research outputs found
Information Spreading in Stationary Markovian Evolving Graphs
Markovian evolving graphs are dynamic-graph models where the links among a
fixed set of nodes change during time according to an arbitrary Markovian rule.
They are extremely general and they can well describe important dynamic-network
scenarios.
We study the speed of information spreading in the "stationary phase" by
analyzing the completion time of the "flooding mechanism". We prove a general
theorem that establishes an upper bound on flooding time in any stationary
Markovian evolving graph in terms of its node-expansion properties.
We apply our theorem in two natural and relevant cases of such dynamic
graphs. "Geometric Markovian evolving graphs" where the Markovian behaviour is
yielded by "n" mobile radio stations, with fixed transmission radius, that
perform independent random walks over a square region of the plane.
"Edge-Markovian evolving graphs" where the probability of existence of any edge
at time "t" depends on the existence (or not) of the same edge at time "t-1".
In both cases, the obtained upper bounds hold "with high probability" and
they are nearly tight. In fact, they turn out to be tight for a large range of
the values of the input parameters. As for geometric Markovian evolving graphs,
our result represents the first analytical upper bound for flooding time on a
class of concrete mobile networks.Comment: 16 page
Common adversaries form alliances: modelling complex networks via anti-transitivity
Anti-transitivity captures the notion that enemies of enemies are friends,
and arises naturally in the study of adversaries in social networks and in the
study of conflicting nation states or organizations. We present a simplified,
evolutionary model for anti-transitivity influencing link formation in complex
networks, and analyze the model's network dynamics. The Iterated Local
Anti-Transitivity (or ILAT) model creates anti-clone nodes in each time-step,
and joins anti-clones to the parent node's non-neighbor set. The graphs
generated by ILAT exhibit familiar properties of complex networks such as
densification, short distances (bounded by absolute constants), and bad
spectral expansion. We determine the cop and domination number for graphs
generated by ILAT, and finish with an analysis of their clustering
coefficients. We interpret these results within the context of real-world
complex networks and present open problems
The statistical mechanics of networks
We study the family of network models derived by requiring the expected
properties of a graph ensemble to match a given set of measurements of a
real-world network, while maximizing the entropy of the ensemble. Models of
this type play the same role in the study of networks as is played by the
Boltzmann distribution in classical statistical mechanics; they offer the best
prediction of network properties subject to the constraints imposed by a given
set of observations. We give exact solutions of models within this class that
incorporate arbitrary degree distributions and arbitrary but independent edge
probabilities. We also discuss some more complex examples with correlated edges
that can be solved approximately or exactly by adapting various familiar
methods, including mean-field theory, perturbation theory, and saddle-point
expansions.Comment: 15 pages, 4 figure
NetLSD: Hearing the Shape of a Graph
Comparison among graphs is ubiquitous in graph analytics. However, it is a
hard task in terms of the expressiveness of the employed similarity measure and
the efficiency of its computation. Ideally, graph comparison should be
invariant to the order of nodes and the sizes of compared graphs, adaptive to
the scale of graph patterns, and scalable. Unfortunately, these properties have
not been addressed together. Graph comparisons still rely on direct approaches,
graph kernels, or representation-based methods, which are all inefficient and
impractical for large graph collections.
In this paper, we propose the Network Laplacian Spectral Descriptor (NetLSD):
the first, to our knowledge, permutation- and size-invariant, scale-adaptive,
and efficiently computable graph representation method that allows for
straightforward comparisons of large graphs. NetLSD extracts a compact
signature that inherits the formal properties of the Laplacian spectrum,
specifically its heat or wave kernel; thus, it hears the shape of a graph. Our
evaluation on a variety of real-world graphs demonstrates that it outperforms
previous works in both expressiveness and efficiency.Comment: KDD '18: The 24th ACM SIGKDD International Conference on Knowledge
Discovery & Data Mining, August 19--23, 2018, London, United Kingdo
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