From neurons to epidemics: How trophic coherence affects spreading processes

Trophic coherence, a measure of the extent to which the nodes of a directed network are organised in levels, has recently been shown to be closely related to many structural and dynamical aspects of complex systems, including graph eigenspectra, the prevalence or absence of feed-back cycles, and linear stability. Furthermore, non-trivial trophic structures have been observed in networks of neurons, species, genes, metabolites, cellular signalling, concatenated words, P2P users, and world trade. Here we consider two simple yet apparently quite different dynamical models -- one a Susceptible-Infected-Susceptible (SIS) epidemic model adapted to include complex contagion, the other an Amari-Hopfield neural network -- and show that in both cases the related spreading processes are modulated in similar ways by the trophic coherence of the underlying networks. To do this, we propose a network assembly model which can generate structures with tunable trophic coherence, limiting in either perfectly stratified networks or random graphs. We find that trophic coherence can exert a qualitative change in spreading behaviour, determining whether a pulse of activity will percolate through the entire network or remain confined to a subset of nodes, and whether such activity will quickly die out or endure indefinitely. These results could be important for our understanding of phenomena such as epidemics, rumours, shocks to ecosystems, neuronal avalanches, and many other spreading processes

Collective decision-making on triadic graphs

Many real-world networks exhibit community structures and non-trivial clustering associated with the occurrence of a considerable number of triangular subgraphs known as triadic motifs. Triads are a set of distinct triangles that do not share an edge with any other triangle in the network. Network motifs are subgraphs that occur significantly more often compared to random topologies. Two prominent examples, the feedforward loop and the feedback loop, occur in various real-world networks such as gene-regulatory networks, food webs or neuronal networks. However, as triangular connections are also prevalent in communication topologies of complex collective systems, it is worthwhile investigating the influence of triadic motifs on the collective decision-making dynamics. To this end, we generate networks called Triadic Graphs (TGs) exclusively from distinct triadic motifs. We then apply TGs as underlying topologies of systems with collective dynamics inspired from locust marching bands. We demonstrate that the motif type constituting the networks can have a paramount influence on group decision-making that cannot be explained solely in terms of the degree distribution. We find that, in contrast to the feedback loop, when the feedforward loop is the dominant subgraph, the resulting network is hierarchical and inhibits coherent behavior