Graph Theory and Networks in Biology

In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape

Network segregation in a model of misinformation and fact checking

Misinformation under the form of rumor, hoaxes, and conspiracy theories spreads on social media at alarming rates. One hypothesis is that, since social media are shaped by homophily, belief in misinformation may be more likely to thrive on those social circles that are segregated from the rest of the network. One possible antidote is fact checking which, in some cases, is known to stop rumors from spreading further. However, fact checking may also backfire and reinforce the belief in a hoax. Here we take into account the combination of network segregation, finite memory and attention, and fact-checking efforts. We consider a compartmental model of two interacting epidemic processes over a network that is segregated between gullible and skeptic users. Extensive simulation and mean-field analysis show that a more segregated network facilitates the spread of a hoax only at low forgetting rates, but has no effect when agents forget at faster rates. This finding may inform the development of mitigation techniques and overall inform on the risks of uncontrolled misinformation online

Evolution equation for a model of surface relaxation in complex networks

In this paper we derive analytically the evolution equation of the interface for a model of surface growth with relaxation to the minimum (SRM) in complex networks. We were inspired by the disagreement between the scaling results of the steady state of the fluctuations between the discrete SRM model and the Edward-Wilkinson process found in scale-free networks with degree distribution $P(k) \sim k^{-\lambda}$ for $\lambda <3$ [Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf 76}, 046117 (2007)]. Even though for Euclidean lattices the evolution equation is linear, we find that in complex heterogeneous networks non-linear terms appear due to the heterogeneity and the lack of symmetry of the network; they produce a logarithmic divergency of the saturation roughness with the system size as found by Pastore y Piontti {\it et al.} for $\lambda <3$.Comment: 9 pages, 2 figure