Simulation
codes and network topologies for the examples in the paper J.P. Gleeson and R.
Durrett, Temporal profiles of avalanches on networks, arXiv:1612.06477. Download
the Octave/MATLAB files here. Please cite the paper if used in
publications; send comments and bug reports to james.gleeson@ul.ie.

Updated:
10 Aug 2017

**Simulation codes:**

The main
simulation codes are as follows:

·
model_memes.m: Script to run simulations of the meme
propagation model of [J.P. Gleeson et al., Phys. Rev. Lett. 112, 048701 (2014);
arXiv:1305.4328].

·
model_neuro.m: Script to run simulations of the neuronal
dynamics model of [N. Friedman et al., Phys. Rev. Lett. 108, 208102 (2012)].

·
model_threshold.m: Script to run simulations of the Centola-Macy threshold model [D. Centola
and M. Macy, J. Sociology, 113, 702 (2007)].

Subsidiary
simulation codes are as follows:

·
model_memes_randrewire.m: Same dynamics as in model_memes.m, but first randomly rewires the network.

·
model_memes_pjkrewire.m: Same dynamics as in model_memes.m, but first rewires the network to retain the
joint distribution of in- and out-degrees, but otherwise randomize the
structure.

·
model_memes_nonMarkovian.m: A continuous-time generalization
of the dynamics of model_memes.m, where each node
waits an inter-event time \tau_n between its tweets,
with \tau_n drawn from a unit-mean Weibull
distribution with shape parameter k and scale parameter lambda=1/Gamma(1+1/k)

**Network topologies: **

Each
network topology file is a MAT file containing a scalar N (number of nodes in
network), and two vectors fromv and tov, which define
the directed edges (i,j) of the unweighted network,
where i=fromv(n) and
j=tov(n), for n=1 to total number of edges.

·
dat_network_directed_powerlaw.mat: Directed configuration-model
network generated by assigning k out-stubs to each node, where k is drawn from
a power-law distribution p_k with exponent 2.5 (and p_k=0 for k<4). Each out-stub is then designated to be
an in-edge of a randomly-chosen node, which means that the in-degree
distributions is Poisson, and the in-degree and the out-degree of a node are
independent. Any self-links or multi-links are deleted.

·
dat_network_directed_zregular.mat: As above, except that the
out-degree distribution p_k has unit mass at k=10,
meaning that every node has out-degree 10.

·
dat_network_undirected_powerlaw.mat: Undirected configuration-model
network generated by assigning k stubs to each node, where k is drawn from a
power-law distribution p_k with exponent 3.3 (and p_k=0 for k<2). Pairs of stubs are then chosen at random
to create the edges of the network. Any self-links or multi-links are deleted.

·
dat_network_undirected_zregular.mat: As above, except that the degree
distribution p_k has unit mass at k=3, meaning that
every node has degree 3.

·
dat_network_directed_SNAPtwitter.mat: Directed network created from
lists on Twitter, using the twitter_combined.txt file available from the SNAP dataset
repository [J. McAuley and J. Leskovec.
Learning to Discover Social Circles in Ego Networks. NIPS, 2012]. We read in
the (i,j) edges from the
twitter_combined.txt file, reindexing the nodes from
1 to N, and delete any self-links or multi-links.

**Examples:**

**To reproduce the simulation results for the
figures in the paper, use the following:**

·
**Fig. 5(a), (c) and (e): Simulations
using model_memes.m, with input file dat_network_directed_powerlaw.mat **

·
**Fig. 5(b), (d) and (f): Simulations
using model_memes.m, with input file dat_network_directed_zregular.mat **

·
**Fig. 6(a), (c) and (e): Simulations
using model_neuro.m, with input file dat_network_directed_powerlaw.mat **

·
**Fig. 6(b), (d) and (f): Simulations
using model_neuro.m, with input file dat_network_directed_zregular.mat **

·
**Fig. 7(a), (c) and (e): Simulations
using model_threshold.m, with input file dat_network_undirected_powerlaw.mat **

·
**Fig. 7(b), (d) and (f): Simulations
using model_threshold.m, with input file dat_network_undirected_zregular.mat **

·
**Fig. 8(a), (c) and (e): Simulations
using model_memes.m, with input file dat_network_directed_SNAPtwitter.mat**

·
**Fig. 8(b), (d) and (f): Simulations
using model_memes_randrewire.m**

·
**Supplementary Fig. 6: Simulations
using model_memes_pjkrewire.m**

·
**Supplementary Fig. 8(a), (c) and
(e): Simulations using model_memes_nonMarkovian.m, with
input file dat_network_directed_powerlaw.mat and
k=0.5**

·
**Supplementary Fig. 8(b), (d) and
(f): Simulations using model_memes_nonMarkovian.m,
with input file dat_network_directed_zregular.mat and
k=0.5**

·
**Supplementary Fig. 9(a), (c) and
(e): Simulations using model_memes_nonMarkovian.m,
with input file dat_network_directed_powerlaw.mat and
k=0.4**

·
**Supplementary Fig. 9(b), (d) and
(f): Simulations using model_memes_nonMarkovian.m,
with input file dat_network_directed_zregular.mat and
k=0.4**

·
**Supplementary Fig. 10(a), (c) and
(e): Simulations using model_memes_nonMarkovian.m,
with input file dat_network_directed_powerlaw.mat and
k=0.3**

·
**Supplementary Fig. 10(b), (d) and
(f): Simulations using model_memes_nonMarkovian.m,
with input file dat_network_directed_zregular.mat and
k=0.3**

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