47,650 research outputs found
Function and form in networks of interacting agents
The main problem we address in this paper is whether function determines form
when a society of agents organizes itself for some purpose or whether the
organizing method is more important than the functionality in determining the
structure of the ensemble. As an example, we use a neural network that learns
the same function by two different learning methods. For sufficiently large
networks, very different structures may indeed be obtained for the same
functionality. Clustering, characteristic path length and hierarchy are
structural differences, which in turn have implications on the robustness and
adaptability of the networks. In networks, as opposed to simple graphs, the
connections between the agents are not necessarily symmetric and may have
positive or negative signs. New characteristic coefficients are introduced to
characterize this richer connectivity structure.Comment: 27 pages Latex, 11 figure
Rainbow Hamilton cycles in random regular graphs
A rainbow subgraph of an edge-coloured graph has all edges of distinct
colours. A random d-regular graph with d even, and having edges coloured
randomly with d/2 of each of n colours, has a rainbow Hamilton cycle with
probability tending to 1 as n tends to infinity, provided d is at least 8.Comment: 16 page
Evolving Social Networks via Friend Recommendations
A social network grows over a period of time with the formation of new
connections and relations. In recent years we have witnessed a massive growth
of online social networks like Facebook, Twitter etc. So it has become a
problem of extreme importance to know the destiny of these networks. Thus
predicting the evolution of a social network is a question of extreme
importance. A good model for evolution of a social network can help in
understanding the properties responsible for the changes occurring in a network
structure. In this paper we propose such a model for evolution of social
networks. We model the social network as an undirected graph where nodes
represent people and edges represent the friendship between them. We define the
evolution process as a set of rules which resembles very closely to how a
social network grows in real life. We simulate the evolution process and show,
how starting from an initial network, a network evolves using this model. We
also discuss how our model can be used to model various complex social networks
other than online social networks like political networks, various
organizations etc..Comment: 5 pages, 8 figures, 2 algorithm
A statistical network analysis of the HIV/AIDS epidemics in Cuba
The Cuban contact-tracing detection system set up in 1986 allowed the
reconstruction and analysis of the sexual network underlying the epidemic
(5,389 vertices and 4,073 edges, giant component of 2,386 nodes and 3,168
edges), shedding light onto the spread of HIV and the role of contact-tracing.
Clustering based on modularity optimization provides a better visualization and
understanding of the network, in combination with the study of covariates. The
graph has a globally low but heterogeneous density, with clusters of high
intraconnectivity but low interconnectivity. Though descriptive, our results
pave the way for incorporating structure when studying stochastic SIR epidemics
spreading on social networks
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