36 research outputs found
Coverage centralities for temporal networks
Structure of real networked systems, such as social relationship, can be
modeled as temporal networks in which each edge appears only at the prescribed
time. Understanding the structure of temporal networks requires quantifying the
importance of a temporal vertex, which is a pair of vertex index and time. In
this paper, we define two centrality measures of a temporal vertex based on the
fastest temporal paths which use the temporal vertex. The definition is free
from parameters and robust against the change in time scale on which we focus.
In addition, we can efficiently compute these centrality values for all
temporal vertices. Using the two centrality measures, we reveal that
distributions of these centrality values of real-world temporal networks are
heterogeneous. For various datasets, we also demonstrate that a majority of the
highly central temporal vertices are located within a narrow time window around
a particular time. In other words, there is a bottleneck time at which most
information sent in the temporal network passes through a small number of
temporal vertices, which suggests an important role of these temporal vertices
in spreading phenomena.Comment: 13 pages, 10 figure
Community detection in directed acyclic graphs
Some temporal networks, most notably citation networks, are naturally
represented as directed acyclic graphs (DAGs). To detect communities in DAGs,
we propose a modularity for DAGs by defining an appropriate null model (i.e.,
randomized network) respecting the order of nodes. We implement a spectral
method to approximately maximize the proposed modularity measure and test the
method on citation networks and other DAGs. We find that the attained values of
the modularity for DAGs are similar for partitions that we obtain by maximizing
the proposed modularity (designed for DAGs), the modularity for undirected
networks and that for general directed networks. In other words, if we neglect
the order imposed on nodes (and the direction of links) in a given DAG and
maximize the conventional modularity measure, the obtained partition is close
to the optimal one in the sense of the modularity for DAGs.Comment: 2 figures, 7 table
Sufficient conditions of endemic threshold on metapopulation networks
In this paper, we focus on susceptible-infected-susceptible dynamics on
metapopulation networks, where nodes represent subpopulations, and where agents
diffuse and interact. Recent studies suggest that heterogeneous network
structure between elements plays an important role in determining the threshold
of infection rate at the onset of epidemics, a fundamental quantity governing
the epidemic dynamics. We consider the general case in which the infection rate
at each node depends on its population size, as shown in recent empirical
observations. We first prove that a sufficient condition for the endemic
threshold (i.e., its upper bound), previously derived based on a mean-field
approximation of network structure, also holds true for arbitrary networks. We
also derive an improved condition showing that networks with the rich-club
property (i.e., high connectivity between nodes with a large number of links)
are more prone to disease spreading. The dependency of infection rate on
population size introduces a considerable difference between this upper bound
and estimates based on mean-field approximations, even when degree-degree
correlations are considered. We verify the theoretical results with numerical
simulations.Comment: 32 pages, 5 figure
Predictability of conversation partners
Recent developments in sensing technologies have enabled us to examine the
nature of human social behavior in greater detail. By applying an information
theoretic method to the spatiotemporal data of cell-phone locations, [C. Song
et al. Science 327, 1018 (2010)] found that human mobility patterns are
remarkably predictable. Inspired by their work, we address a similar
predictability question in a different kind of human social activity:
conversation events. The predictability in the sequence of one's conversation
partners is defined as the degree to which one's next conversation partner can
be predicted given the current partner. We quantify this predictability by
using the mutual information. We examine the predictability of conversation
events for each individual using the longitudinal data of face-to-face
interactions collected from two company offices in Japan. Each subject wears a
name tag equipped with an infrared sensor node, and conversation events are
marked when signals are exchanged between sensor nodes in close proximity. We
find that the conversation events are predictable to some extent; knowing the
current partner decreases the uncertainty about the next partner by 28.4% on
average. Much of the predictability is explained by long-tailed distributions
of interevent intervals. However, a predictability also exists in the data,
apart from the contribution of their long-tailed nature. In addition, an
individual's predictability is correlated with the position in the static
social network derived from the data. Individuals confined in a community - in
the sense of an abundance of surrounding triangles - tend to have low
predictability, and those bridging different communities tend to have high
predictability.Comment: 38 pages, 19 figure