710 research outputs found
Structure of Heterogeneous Networks
Heterogeneous networks play a key role in the evolution of communities and
the decisions individuals make. These networks link different types of
entities, for example, people and the events they attend. Network analysis
algorithms usually project such networks unto simple graphs composed of
entities of a single type. In the process, they conflate relations between
entities of different types and loose important structural information. We
develop a mathematical framework that can be used to compactly represent and
analyze heterogeneous networks that combine multiple entity and link types. We
generalize Bonacich centrality, which measures connectivity between nodes by
the number of paths between them, to heterogeneous networks and use this
measure to study network structure. Specifically, we extend the popular
modularity-maximization method for community detection to use this centrality
metric. We also rank nodes based on their connectivity to other nodes. One
advantage of this centrality metric is that it has a tunable parameter we can
use to set the length scale of interactions. By studying how rankings change
with this parameter allows us to identify important nodes in the network. We
apply the proposed method to analyze the structure of several heterogeneous
networks. We show that exploiting additional sources of evidence corresponding
to links between, as well as among, different entity types yields new insights
into network structure
Benchmarking Measures of Network Influence
Identifying key agents for the transmission of diseases (ideas, technology,
etc.) across social networks has predominantly relied on measures of centrality
on a static base network or a temporally flattened graph of agent interactions.
Various measures have been proposed as the best trackers of influence, such as
degree centrality, betweenness, and -shell, depending on the structure of
the connectivity. We consider SIR and SIS propagation dynamics on a
temporally-extruded network of observed interactions and measure the
conditional marginal spread as the change in the magnitude of the infection
given the removal of each agent at each time: its temporal knockout (TKO)
score. We argue that the exhaustive approach of the TKO score makes it an
effective benchmark measure for evaluating the accuracy of other, often more
practical, measures of influence. We find that none of the common network
measures applied to the induced flat graphs are accurate predictors of network
propagation influence on the systems studied; however, temporal networks and
the TKO measure provide the requisite targets for the hunt for effective
predictive measures
Contextual Centrality: Going Beyond Network Structures
Centrality is a fundamental network property which ranks nodes by their
structural importance. However, structural importance may not suffice to
predict successful diffusions in a wide range of applications, such as
word-of-mouth marketing and political campaigns. In particular, nodes with high
structural importance may contribute negatively to the objective of the
diffusion. To address this problem, we propose contextual centrality, which
integrates structural positions, the diffusion process, and, most importantly,
nodal contributions to the objective of the diffusion. We perform an empirical
analysis of the adoption of microfinance in Indian villages and weather
insurance in Chinese villages. Results show that contextual centrality of the
first-informed individuals has higher predictive power towards the eventual
adoption outcomes than other standard centrality measures. Interestingly, when
the product of diffusion rate and the largest eigenvalue is
larger than one and diffusion period is long, contextual centrality linearly
scales with eigenvector centrality. This approximation reveals that contextual
centrality identifies scenarios where a higher diffusion rate of individuals
may negatively influence the cascade payoff. Further simulations on the
synthetic and real-world networks show that contextual centrality has the
advantage of selecting an individual whose local neighborhood generates a high
cascade payoff when . Under this condition, stronger homophily
leads to higher cascade payoff. Our results suggest that contextual centrality
captures more complicated dynamics on networks and has significant implications
for applications, such as information diffusion, viral marketing, and political
campaigns
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