2,061 research outputs found
Centrality and spectral radius in dynamic communication networks
We explore the influence of the choice of attenuation factor on Katz centrality indices for evolving communication networks. For given snapshots of a network observed over a period of time, recently developed communicability indices aim to identify best broadcasters and listeners in the network. In this article, we looked into the sensitivity of communicability indices on the attenuation factor constraint, in relation to spectral radius (the largest eigenvalue) of the network at any point in time and its computation in the case of large networks. We proposed relaxed communicability measures where the spectral radius bound on attenuation factor is relaxed and the adjacency matrix is normalised in order to maintain the convergence of the measure. Using a vitality based measure of both standard and relaxed communicability indices we looked at the ways of establishing the most important individuals for broadcasting and receiving of messages related to community bridging roles. We illustrated our findings with two examples of real-life networks, MIT reality mining data set of daily communications between 106 individuals during one year and UK Twitter mentions network, direct messages on Twitter between 12.4k individuals during one week
Optimal Vaccine Allocation to Control Epidemic Outbreaks in Arbitrary Networks
We consider the problem of controlling the propagation of an epidemic
outbreak in an arbitrary contact network by distributing vaccination resources
throughout the network. We analyze a networked version of the
Susceptible-Infected-Susceptible (SIS) epidemic model when individuals in the
network present different levels of susceptibility to the epidemic. In this
context, controlling the spread of an epidemic outbreak can be written as a
spectral condition involving the eigenvalues of a matrix that depends on the
network structure and the parameters of the model. We study the problem of
finding the optimal distribution of vaccines throughout the network to control
the spread of an epidemic outbreak. We propose a convex framework to find
cost-optimal distribution of vaccination resources when different levels of
vaccination are allowed. We also propose a greedy approach with quality
guarantees for the case of all-or-nothing vaccination. We illustrate our
approaches with numerical simulations in a real social network
A network approach for power grid robustness against cascading failures
Cascading failures are one of the main reasons for blackouts in electrical
power grids. Stable power supply requires a robust design of the power grid
topology. Currently, the impact of the grid structure on the grid robustness is
mainly assessed by purely topological metrics, that fail to capture the
fundamental properties of the electrical power grids such as power flow
allocation according to Kirchhoff's laws. This paper deploys the effective
graph resistance as a metric to relate the topology of a grid to its robustness
against cascading failures. Specifically, the effective graph resistance is
deployed as a metric for network expansions (by means of transmission line
additions) of an existing power grid. Four strategies based on network
properties are investigated to optimize the effective graph resistance,
accordingly to improve the robustness, of a given power grid at a low
computational complexity. Experimental results suggest the existence of
Braess's paradox in power grids: bringing an additional line into the system
occasionally results in decrease of the grid robustness. This paper further
investigates the impact of the topology on the Braess's paradox, and identifies
specific sub-structures whose existence results in Braess's paradox. Careful
assessment of the design and expansion choices of grid topologies incorporating
the insights provided by this paper optimizes the robustness of a power grid,
while avoiding the Braess's paradox in the system.Comment: 7 pages, 13 figures conferenc
A survey on Human Mobility and its applications
Human Mobility has attracted attentions from different fields of studies such
as epidemic modeling, traffic engineering, traffic prediction and urban
planning. In this survey we review major characteristics of human mobility
studies including from trajectory-based studies to studies using graph and
network theory. In trajectory-based studies statistical measures such as jump
length distribution and radius of gyration are analyzed in order to investigate
how people move in their daily life, and if it is possible to model this
individual movements and make prediction based on them. Using graph in mobility
studies, helps to investigate the dynamic behavior of the system, such as
diffusion and flow in the network and makes it easier to estimate how much one
part of the network influences another by using metrics like centrality
measures. We aim to study population flow in transportation networks using
mobility data to derive models and patterns, and to develop new applications in
predicting phenomena such as congestion. Human Mobility studies with the new
generation of mobility data provided by cellular phone networks, arise new
challenges such as data storing, data representation, data analysis and
computation complexity. A comparative review of different data types used in
current tools and applications of Human Mobility studies leads us to new
approaches for dealing with mentioned challenges
Correlation between centrality metrics and their application to the opinion model
In recent decades, a number of centrality metrics describing network
properties of nodes have been proposed to rank the importance of nodes. In
order to understand the correlations between centrality metrics and to
approximate a high-complexity centrality metric by a strongly correlated
low-complexity metric, we first study the correlation between centrality
metrics in terms of their Pearson correlation coefficient and their similarity
in ranking of nodes. In addition to considering the widely used centrality
metrics, we introduce a new centrality measure, the degree mass. The m order
degree mass of a node is the sum of the weighted degree of the node and its
neighbors no further than m hops away. We find that the B_{n}, the closeness,
and the components of x_{1} are strongly correlated with the degree, the
1st-order degree mass and the 2nd-order degree mass, respectively, in both
network models and real-world networks. We then theoretically prove that the
Pearson correlation coefficient between x_{1} and the 2nd-order degree mass is
larger than that between x_{1} and a lower order degree mass. Finally, we
investigate the effect of the inflexible antagonists selected based on
different centrality metrics in helping one opinion to compete with another in
the inflexible antagonists opinion model. Interestingly, we find that selecting
the inflexible antagonists based on the leverage, the B_{n}, or the degree is
more effective in opinion-competition than using other centrality metrics in
all types of networks. This observation is supported by our previous
observations, i.e., that there is a strong linear correlation between the
degree and the B_{n}, as well as a high centrality similarity between the
leverage and the degree.Comment: 20 page
On the radius of centrality in evolving communication networks
In this article, we investigate how the choice of the attenuation factor in an extended version of Katz centrality influences the centrality of the nodes in evolving communication networks. For given snapshots of a network, observed over a period of time, recently developed communicability indices aim to identify the best broadcasters and listeners (receivers) in the network. Here we explore the attenuation factor constraint, in relation to the spectral radius (the largest eigenvalue) of the network at any point in time and its computation in the case of large networks. We compare three different communicability measures: standard, exponential, and relaxed (where the spectral radius bound on the attenuation factor is relaxed and the adjacency matrix is normalised, in order to maintain the convergence of the measure). Furthermore, using a vitality-based measure of both standard and relaxed communicability indices, we look at the ways of establishing the most important individuals for broadcasting and receiving of messages related to community bridging roles. We compare those measures with the scores produced by an iterative version of the PageRank algorithm and illustrate our findings with two examples of real-life evolving networks: the MIT reality mining data set, consisting of daily communications between 106 individuals over the period of one year, a UK Twitter mentions network, constructed from the direct \emph{tweets} between 12.4k individuals during one week, and a subset the Enron email data set
- …