19 citations · 84 across the 10 of their papers we have counts for
10 papers
Degree correlations in graphs with clique clustering
Peter Mann, V. Anne Smith, John B. O. Mitchell +1
Correlations among the degrees of vertices in random graphs often occur when clustering is present. In this paper we define a joint-degree correlation function for vertices in the…
An exact N-strain epidemic model using bond percolation
Peter Mann, V. Anne Smith, John B. O. Mitchell +1
In this paper we examine the emergent structures of random networks that have undergone bond percolation an arbitrary, but finite, number of times. We define two types of sequentia…
Symbiotic and antagonistic disease dynamics on networks using bond percolatio
Peter Mann, V. Anne Smith, John Mitchell +1
In this paper we introduce a novel description of the equilibrium state of a bond percolation process on random graphs using the exact method of generating functions. This allows u…
Belief propagation on networks with cliques and chordless cycles
Peter Mann, Simon Dobson
It is well known that tree-based theories can describe the properties of undirected clustered networks with extremely accurate results [S. Melnik, \textit{et al}. Phys. Rev. E 83,…
Mixing patterns in graphs with higher-order structure
Peter Mann, Lei Fang, Simon Dobson
In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to con…
An exact formula for percolation on higher-order cycles
Peter Mann, V Anne Smith, John Mitchell +2
We present exact solutions for the size of the giant connected component (GCC) of graphs composed of higher-order homogeneous cycles, including weak cycles and cliques, following b…
Cooperative coinfection dynamics on clustered networks
Peter Mann, Anne Smith, John Mitchell +1
Coinfection is the process by which a host that is infected with a pathogen becomes infected by a second pathogen at a later point in time. An immunosuppressant host response to a…
Two-pathogen model with competition on clustered networks
Peter Mann, V. Anne Smith, John B. O. Mitchell +1
Networks provide a mathematically rich framework to represent social contacts sufficient for the transmission of disease. Social networks are often highly clustered and fail to be…
Random graphs with arbitrary clustering and their applications
Peter Mann, V. Anne Smith, John B. O. Mitchell +1
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A.…
Percolation in random graphs with higher-order clustering
Peter Mann, V. Anne Smith, John B. O. Mitchell +1
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally…