21,492 research outputs found
Centrality Metric for Dynamic Networks
Centrality is an important notion in network analysis and is used to measure
the degree to which network structure contributes to the importance of a node
in a network. While many different centrality measures exist, most of them
apply to static networks. Most networks, on the other hand, are dynamic in
nature, evolving over time through the addition or deletion of nodes and edges.
A popular approach to analyzing such networks represents them by a static
network that aggregates all edges observed over some time period. This
approach, however, under or overestimates centrality of some nodes. We address
this problem by introducing a novel centrality metric for dynamic network
analysis. This metric exploits an intuition that in order for one node in a
dynamic network to influence another over some period of time, there must exist
a path that connects the source and destination nodes through intermediaries at
different times. We demonstrate on an example network that the proposed metric
leads to a very different ranking than analysis of an equivalent static
network. We use dynamic centrality to study a dynamic citations network and
contrast results to those reached by static network analysis.Comment: in KDD workshop on Mining and Learning in Graphs (MLG
Understanding the spreading power of all nodes in a network: a continuous-time perspective
Centrality measures such as the degree, k-shell, or eigenvalue centrality can
identify a network's most influential nodes, but are rarely usefully accurate
in quantifying the spreading power of the vast majority of nodes which are not
highly influential. The spreading power of all network nodes is better
explained by considering, from a continuous-time epidemiological perspective,
the distribution of the force of infection each node generates. The resulting
metric, the \textit{expected force}, accurately quantifies node spreading power
under all primary epidemiological models across a wide range of archetypical
human contact networks. When node power is low, influence is a function of
neighbor degree. As power increases, a node's own degree becomes more
important. The strength of this relationship is modulated by network structure,
being more pronounced in narrow, dense networks typical of social networking
and weakening in broader, looser association networks such as the Internet. The
expected force can be computed independently for individual nodes, making it
applicable for networks whose adjacency matrix is dynamic, not well specified,
or overwhelmingly large
Non-Conservative Diffusion and its Application to Social Network Analysis
The random walk is fundamental to modeling dynamic processes on networks.
Metrics based on the random walk have been used in many applications from image
processing to Web page ranking. However, how appropriate are random walks to
modeling and analyzing social networks? We argue that unlike a random walk,
which conserves the quantity diffusing on a network, many interesting social
phenomena, such as the spread of information or disease on a social network,
are fundamentally non-conservative. When an individual infects her neighbor
with a virus, the total amount of infection increases. We classify diffusion
processes as conservative and non-conservative and show how these differences
impact the choice of metrics used for network analysis, as well as our
understanding of network structure and behavior. We show that Alpha-Centrality,
which mathematically describes non-conservative diffusion, leads to new
insights into the behavior of spreading processes on networks. We give a
scalable approximate algorithm for computing the Alpha-Centrality in a massive
graph. We validate our approach on real-world online social networks of Digg.
We show that a non-conservative metric, such as Alpha-Centrality, produces
better agreement with empirical measure of influence than conservative metrics,
such as PageRank. We hope that our investigation will inspire further
exploration into the realms of conservative and non-conservative metrics in
social network analysis
Incremental closeness centrality in distributed memory
Networks are commonly used to model traffic patterns, social interactions, or web pages. The vertices in a network do not possess the same characteristics: some vertices are naturally more connected and some vertices can be more important. Closeness centrality (CC) is a global metric that quantifies how important is a given vertex in the network. When the network is dynamic and keeps changing, the relative importance of the vertices also changes. The best known algorithm to compute the CC scores makes it impractical to recompute them from scratch after each modification. In this paper, we propose Streamer, a distributed memory framework for incrementally maintaining the closeness centrality scores of a network upon changes. It leverages pipelined, replicated parallelism, and SpMM-based BFSs, and it takes NUMA effects into account. It makes maintaining the Closeness Centrality values of real-life networks with millions of interactions significantly faster and obtains almost linear speedups on a 64 nodes 8 threads/node cluster
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