724,615 research outputs found
Temporal Networks
A great variety of systems in nature, society and technology -- from the web
of sexual contacts to the Internet, from the nervous system to power grids --
can be modeled as graphs of vertices coupled by edges. The network structure,
describing how the graph is wired, helps us understand, predict and optimize
the behavior of dynamical systems. In many cases, however, the edges are not
continuously active. As an example, in networks of communication via email,
text messages, or phone calls, edges represent sequences of instantaneous or
practically instantaneous contacts. In some cases, edges are active for
non-negligible periods of time: e.g., the proximity patterns of inpatients at
hospitals can be represented by a graph where an edge between two individuals
is on throughout the time they are at the same ward. Like network topology, the
temporal structure of edge activations can affect dynamics of systems
interacting through the network, from disease contagion on the network of
patients to information diffusion over an e-mail network. In this review, we
present the emergent field of temporal networks, and discuss methods for
analyzing topological and temporal structure and models for elucidating their
relation to the behavior of dynamical systems. In the light of traditional
network theory, one can see this framework as moving the information of when
things happen from the dynamical system on the network, to the network itself.
Since fundamental properties, such as the transitivity of edges, do not
necessarily hold in temporal networks, many of these methods need to be quite
different from those for static networks
Temporal interactions facilitate endemicity in the susceptible-infected-susceptible epidemic model
Data of physical contacts and face-to-face communications suggest temporally
varying networks as the media on which infections take place among humans and
animals. Epidemic processes on temporal networks are complicated by complexity
of both network structure and temporal dimensions. Theoretical approaches are
much needed for identifying key factors that affect dynamics of epidemics. In
particular, what factors make some temporal networks stronger media of
infection than other temporal networks is under debate. We develop a theory to
understand the susceptible-infected-susceptible epidemic model on arbitrary
temporal networks, where each contact is used for a finite duration. We show
that temporality of networks lessens the epidemic threshold such that
infections persist more easily in temporal networks than in their static
counterparts. We further show that the Lie commutator bracket of the adjacency
matrices at different times is a key determinant of the epidemic threshold in
temporal networks. The effect of temporality on the epidemic threshold, which
depends on a data set, is approximately predicted by the magnitude of a
commutator norm.Comment: 8 figures, 1 tabl
Motifs in Temporal Networks
Networks are a fundamental tool for modeling complex systems in a variety of
domains including social and communication networks as well as biology and
neuroscience. Small subgraph patterns in networks, called network motifs, are
crucial to understanding the structure and function of these systems. However,
the role of network motifs in temporal networks, which contain many timestamped
links between the nodes, is not yet well understood.
Here we develop a notion of a temporal network motif as an elementary unit of
temporal networks and provide a general methodology for counting such motifs.
We define temporal network motifs as induced subgraphs on sequences of temporal
edges, design fast algorithms for counting temporal motifs, and prove their
runtime complexity. Our fast algorithms achieve up to 56.5x speedup compared to
a baseline method. Furthermore, we use our algorithms to count temporal motifs
in a variety of networks. Results show that networks from different domains
have significantly different motif counts, whereas networks from the same
domain tend to have similar motif counts. We also find that different motifs
occur at different time scales, which provides further insights into structure
and function of temporal networks
Higher-Order Aggregate Networks in the Analysis of Temporal Networks: Path structures and centralities
Recent research on temporal networks has highlighted the limitations of a
static network perspective for our understanding of complex systems with
dynamic topologies. In particular, recent works have shown that i) the specific
order in which links occur in real-world temporal networks affects causality
structures and thus the evolution of dynamical processes, and ii) higher-order
aggregate representations of temporal networks can be used to analytically
study the effect of these order correlations on dynamical processes. In this
article we analyze the effect of order correlations on path-based centrality
measures in real-world temporal networks. Analyzing temporal equivalents of
betweenness, closeness and reach centrality in six empirical temporal networks,
we first show that an analysis of the commonly used static, time-aggregated
representation can give misleading results about the actual importance of
nodes. We further study higher-order time-aggregated networks, a recently
proposed generalization of the commonly applied static, time-aggregated
representation of temporal networks. Here, we particularly define path-based
centrality measures based on second-order aggregate networks, empirically
validating that node centralities calculated in this way better capture the
true temporal centralities of nodes than node centralities calculated based on
the commonly used static (first-order) representation. Apart from providing a
simple and practical method for the approximation of path-based centralities in
temporal networks, our results highlight interesting perspectives for the use
of higher-order aggregate networks in the analysis of time-stamped network
data.Comment: 27 pages, 13 figures, 3 table
A Generalized Notion of Time for Modeling Temporal Networks
Most approaches for modeling and analyzing temporal networks do not explicitly discuss the underlying notion
of time. In this paper, we therefore introduce a generalized notion of time for temporal networks. Our
approach also allows for considering non-deterministic time and incomplete data, two issues that are often
found when analyzing data-sets extracted from online social networks, for example. In order to demonstrate
the consequences of our generalized notion of time, we also discuss the implications for the computation of
(shortest) temporal paths in temporal networks
Communicability in temporal networks
A first-principles approach to quantify the communicability between pairs of nodes in temporal networks is proposed. It corresponds to the imaginary-time propagator of a quantum random walk in the temporal network, which accounts for unique structural and temporal characteristics of both streaming and nonstreaming temporal networks. The influence of the system's temperature on the perdurability of information and how the communicability identifies patterns of communication hidden in the temporal and topological structure of the networks are also studied for synthetic and real-world systems
Graph Metrics for Temporal Networks
Temporal networks, i.e., networks in which the interactions among a set of
elementary units change over time, can be modelled in terms of time-varying
graphs, which are time-ordered sequences of graphs over a set of nodes. In such
graphs, the concepts of node adjacency and reachability crucially depend on the
exact temporal ordering of the links. Consequently, all the concepts and
metrics proposed and used for the characterisation of static complex networks
have to be redefined or appropriately extended to time-varying graphs, in order
to take into account the effects of time ordering on causality. In this chapter
we discuss how to represent temporal networks and we review the definitions of
walks, paths, connectedness and connected components valid for graphs in which
the links fluctuate over time. We then focus on temporal node-node distance,
and we discuss how to characterise link persistence and the temporal
small-world behaviour in this class of networks. Finally, we discuss the
extension of classic centrality measures, including closeness, betweenness and
spectral centrality, to the case of time-varying graphs, and we review the work
on temporal motifs analysis and the definition of modularity for temporal
graphs.Comment: 26 pages, 5 figures, Chapter in Temporal Networks (Petter Holme and
Jari Saram\"aki editors). Springer. Berlin, Heidelberg 201
Random Walks on Stochastic Temporal Networks
In the study of dynamical processes on networks, there has been intense focus
on network structure -- i.e., the arrangement of edges and their associated
weights -- but the effects of the temporal patterns of edges remains poorly
understood. In this chapter, we develop a mathematical framework for random
walks on temporal networks using an approach that provides a compromise between
abstract but unrealistic models and data-driven but non-mathematical
approaches. To do this, we introduce a stochastic model for temporal networks
in which we summarize the temporal and structural organization of a system
using a matrix of waiting-time distributions. We show that random walks on
stochastic temporal networks can be described exactly by an
integro-differential master equation and derive an analytical expression for
its asymptotic steady state. We also discuss how our work might be useful to
help build centrality measures for temporal networks.Comment: Chapter in Temporal Networks (Petter Holme and Jari Saramaki
editors). Springer. Berlin, Heidelberg 2013. The book chapter contains minor
corrections and modifications. This chapter is based on arXiv:1112.3324,
which contains additional calculations and numerical simulation
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