90 research outputs found
On Exploring Temporal Graphs of Small Pathwidth
We show that the Temporal Graph Exploration Problem is NP-complete, even when
the underlying graph has pathwidth 2 and at each time step, the current graph
is connected
Quantifying Social Network Dynamics
The dynamic character of most social networks requires to model evolution of
networks in order to enable complex analysis of theirs dynamics. The following
paper focuses on the definition of differences between network snapshots by
means of Graph Differential Tuple. These differences enable to calculate the
diverse distance measures as well as to investigate the speed of changes. Four
separate measures are suggested in the paper with experimental study on real
social network data.Comment: In proceedings of the 4th International Conference on Computational
Aspects of Social Networks, CASoN 201
Counting Causal Paths in Big Times Series Data on Networks
Graph or network representations are an important foundation for data mining
and machine learning tasks in relational data. Many tools of network analysis,
like centrality measures, information ranking, or cluster detection rest on the
assumption that links capture direct influence, and that paths represent
possible indirect influence. This assumption is invalidated in time-stamped
network data capturing, e.g., dynamic social networks, biological sequences or
financial transactions. In such data, for two time-stamped links (A,B) and
(B,C) the chronological ordering and timing determines whether a causal path
from node A via B to C exists. A number of works has shown that for that reason
network analysis cannot be directly applied to time-stamped network data.
Existing methods to address this issue require statistics on causal paths,
which is computationally challenging for big data sets.
Addressing this problem, we develop an efficient algorithm to count causal
paths in time-stamped network data. Applying it to empirical data, we show that
our method is more efficient than a baseline method implemented in an
OpenSource data analytics package. Our method works efficiently for different
values of the maximum time difference between consecutive links of a causal
path and supports streaming scenarios. With it, we are closing a gap that
hinders an efficient analysis of big time series data on complex networks.Comment: 10 pages, 2 figure
On analysis of complex network dynamics – changes in local topology
Social networks created based on data gathered in various computer systems are structures that constantly evolve. The nodes and their connections change because they are influenced by the external to the network events.. In this work we present a new approach to the description and quantification of patterns of complex dynamic social networks illustrated with the data from the Wroclaw University of Technology email dataset. We propose an approach based on discovery of local network connection patterns (in this case triads of nodes) as well as we measure and analyse their transitions during network evolution. We define the Triad Transition Matrix (TTM) containing the probabilities of transitions between triads, after that we show how it can help to discover the dynamic patterns of network evolution. One of the main issues when investigating the dynamical process is the selection of the time window size. Thus, the goal of this paper is also to investigate how the size of time window influences the shape of TTM and how the dynamics of triad number change depending on the window size. We have shown that, however the link stability in the network is low, the dynamic network evolution pattern expressed by the TTMs is relatively stable, and thus forming a background for fine-grained classification of complex networks dynamics. Our results open also vast possibilities of link and structure prediction of dynamic networks. The future research and applications stemming from our approach are also proposed and discussed
Link Prediction Based on Subgraph Evolution in Dynamic Social Networks
We propose a new method for characterizing the dynamics of complex networks with its application to the link prediction problem. Our approach is based on the discovery of network subgraphs (in this study: triads of nodes) and measuring their transitions during network evolution. We define the Triad Transition Matrix (TTM) containing the probabilities of transitions between triads found in the network, then we show how it can help to discover and quantify the dynamic patterns of network evolution. We also propose the application of TTM to link prediction with an algorithm (called TTM-predictor) which shows good performance, especially for sparse networks analyzed in short time scales. The future applications and research directions of our approach are also proposed and discussed
Reliable Communication in a Dynamic Network in the Presence of Byzantine Faults
We consider the following problem: two nodes want to reliably communicate in
a dynamic multihop network where some nodes have been compromised, and may have
a totally arbitrary and unpredictable behavior. These nodes are called
Byzantine. We consider the two cases where cryptography is available and not
available. We prove the necessary and sufficient condition (that is, the
weakest possible condition) to ensure reliable communication in this context.
Our proof is constructive, as we provide Byzantine-resilient algorithms for
reliable communication that are optimal with respect to our impossibility
results. In a second part, we investigate the impact of our conditions in three
case studies: participants interacting in a conference, robots moving on a grid
and agents in the subway. Our simulations indicate a clear benefit of using our
algorithms for reliable communication in those contexts
Network reachability of real-world contact sequences
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 tend to decrease
the reachability, and that the order of the contacts really do make sense for
dynamical spreading processes.Comment: (v2: fig. 1 fixed
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
Moving in temporal graphs with very sparse random availability of edges
In this work we consider temporal graphs, i.e. graphs, each edge of which is
assigned a set of discrete time-labels drawn from a set of integers. The labels
of an edge indicate the discrete moments in time at which the edge is
available. We also consider temporal paths in a temporal graph, i.e. paths
whose edges are assigned a strictly increasing sequence of labels. Furthermore,
we assume the uniform case (UNI-CASE), in which every edge of a graph is
assigned exactly one time label from a set of integers and the time labels
assigned to the edges of the graph are chosen randomly and independently, with
the selection following the uniform distribution. We call uniform random
temporal graphs the graphs that satisfy the UNI-CASE. We begin by deriving the
expected number of temporal paths of a given length in the uniform random
temporal clique. We define the term temporal distance of two vertices, which is
the arrival time, i.e. the time-label of the last edge, of the temporal path
that connects those vertices, which has the smallest arrival time amongst all
temporal paths that connect those vertices. We then propose and study two
statistical properties of temporal graphs. One is the maximum expected temporal
distance which is, as the term indicates, the maximum of all expected temporal
distances in the graph. The other one is the temporal diameter which, loosely
speaking, is the expectation of the maximum temporal distance in the graph. We
derive the maximum expected temporal distance of a uniform random temporal star
graph as well as an upper bound on both the maximum expected temporal distance
and the temporal diameter of the normalized version of the uniform random
temporal clique, in which the largest time-label available equals the number of
vertices. Finally, we provide an algorithm that solves an optimization problem
on a specific type of temporal (multi)graphs of two vertices.Comment: 30 page
- …