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

Codes from adjacency matrices of uniform subset graphs

Studies of the p-ary codes from the adjacency matrices of uniform subset graphs Γ(n,k,r)Γ(n,k,r) and their reflexive associates have shown that a particular family of codes defined on the subsets are intimately related to the codes from these graphs. We describe these codes here and examine their relation to some particular classes of uniform subset graphs. In particular we include a complete analysis of the p-ary codes from Γ(n,3,r)Γ(n,3,r) for p≥5p≥5 , thus extending earlier results for p=2,3p=2,3

Round-robin tournaments generated by the circle method have maximum carry-over

The Circle Method is widely used in the field of sport scheduling to generate schedules for round-robin tournaments. The so-called carry-over effect value is a number that can be associated to each round-robin schedule; it represents a degree of balance of a schedule. Here, we prove that, for an even number of teams, the Circle Method generates a schedule with maximum carry-over effect value, answering an open question