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"""
.. _model-dgmg:
Generative Models of Graphs
===========================================
**Author**: `Mufei Li <https://github.com/mufeili>`_,
`Lingfan Yu <https://github.com/ylfdq1118>`_, Zheng Zhang
.. warning::
The tutorial aims at gaining insights into the paper, with code as a mean
of explanation. The implementation thus is NOT optimized for running
efficiency. For recommended implementation, please refer to the `official
examples <https://github.com/dmlc/dgl/tree/master/examples>`_.
"""
##############################################################################
#
# In this tutorial, you learn how to train and generate one graph at
# a time. You also explore parallelism within the graph embedding operation, which is an
# essential building block. The tutorial ends with a simple optimization that
# delivers double the speed by batching across graphs.
#
# Earlier tutorials showed how embedding a graph or
# a node enables you to work on tasks such as `semi-supervised classification for nodes
# <http://docs.dgl.ai/tutorials/models/1_gcn.html#sphx-glr-tutorials-models-1-gcn-py>`__
# or `sentiment analysis
# <http://docs.dgl.ai/tutorials/models/3_tree-lstm.html#sphx-glr-tutorials-models-3-tree-lstm-py>`__.
# Wouldn't it be interesting to predict the future evolution of the graph and
# perform the analysis iteratively?
#
# To address the evolution of the graphs, you generate a variety of graph samples. In other words, you need
# **generative models** of graphs. In-addition to learning
# node and edge features, you would need to model the distribution of arbitrary graphs.
# While general generative models can model the density function explicitly and
# implicitly and generate samples at once or sequentially, you only focus
# on explicit generative models for sequential generation here. Typical applications
# include drug or materials discovery, chemical processes, or proteomics.
#
# Introduction
# --------------------
# The primitive actions of mutating a graph in Deep Graph Library (DGL) are nothing more than ``add_nodes``
# and ``add_edges``. That is, if you were to draw a circle of three nodes,
#
# .. figure:: https://user-images.githubusercontent.com/19576924/48313438-78baf000-e5f7-11e8-931e-cd00ab34fa50.gif
# :alt:
#
# you can write the code as follows.
#
import os
os.environ["DGLBACKEND"] = "pytorch"
import dgl
g = dgl.DGLGraph()
g.add_nodes(1) # Add node 0
g.add_nodes(1) # Add node 1
# Edges in DGLGraph are directed by default.
# For undirected edges, add edges for both directions.
g.add_edges([1, 0], [0, 1]) # Add edges (1, 0), (0, 1)
g.add_nodes(1) # Add node 2
g.add_edges([2, 1], [1, 2]) # Add edges (2, 1), (1, 2)
g.add_edges([2, 0], [0, 2]) # Add edges (2, 0), (0, 2)
#######################################################################################
# Real-world graphs are much more complex. There are many families of graphs,
# with different sizes, topologies, node types, edge types, and the possibility
# of multigraphs. Besides, a same graph can be generated in many different
# orders. Regardless, the generative process entails a few steps.
#
# - Encode a changing graph.
# - Perform actions stochastically.
# - If you are training, collect error signals and optimize the model parameters.
#
# When it comes to implementation, another important aspect is speed. How do you
# parallelize the computation, given that generating a graph is fundamentally a
# sequential process?
#
# .. note::
#
# To be sure, this is not necessarily a hard constraint. Subgraphs can be
# built in parallel and then get assembled. But we
# will restrict ourselves to the sequential processes for this tutorial.
#
#
# DGMG: The main flow
# --------------------
# For this tutorial, you use
# `Deep Generative Models of Graphs <https://arxiv.org/abs/1803.03324>`__
# ) (DGMG) to implement a graph generative model using DGL. Its algorithmic
# framework is general but also challenging to parallelize.
#
# .. note::
#
# While it's possible for DGMG to handle complex graphs with typed nodes,
# typed edges, and multigraphs, here you use a simplified version of it
# for generating graph topologies.
#
# DGMG generates a graph by following a state machine, which is basically a
# two-level loop. Generate one node at a time and connect it to a subset of
# the existing nodes, one at a time. This is similar to language modeling. The
# generative process is an iterative one that emits one word or character or sentence
# at a time, conditioned on the sequence generated so far.
#
# At each time step, you either:
# - Add a new node to the graph
# - Select two existing nodes and add an edge between them
#
# .. figure:: https://user-images.githubusercontent.com/19576924/48605003-7f11e900-e9b6-11e8-8880-87362348e154.png
# :alt:
#
# The Python code will look as follows. In fact, this is *exactly* how inference
# with DGMG is implemented in DGL.
#
def forward_inference(self):
stop = self.add_node_and_update()
while (not stop) and (self.g.num_nodes() < self.v_max + 1):
num_trials = 0
to_add_edge = self.add_edge_or_not()
while to_add_edge and (num_trials < self.g.num_nodes() - 1):
self.choose_dest_and_update()
num_trials += 1
to_add_edge = self.add_edge_or_not()
stop = self.add_node_and_update()
return self.g
#######################################################################################
# Assume you have a pre-trained model for generating cycles of nodes 10-20.
# How does it generate a cycle on-the-fly during inference? Use the code below
# to create an animation with your own model.
#
# ::
#
# import torch
# import matplotlib.animation as animation
# import matplotlib.pyplot as plt
# import networkx as nx
# from copy import deepcopy
#
# if __name__ == '__main__':
# # pre-trained model saved with path ./model.pth
# model = torch.load('./model.pth')
# model.eval()
# g = model()
#
# src_list = g.edges()[1]
# dest_list = g.edges()[0]
#
# evolution = []
#
# nx_g = nx.Graph()
# evolution.append(deepcopy(nx_g))
#
# for i in range(0, len(src_list), 2):
# src = src_list[i].item()
# dest = dest_list[i].item()
# if src not in nx_g.nodes():
# nx_g.add_node(src)
# evolution.append(deepcopy(nx_g))
# if dest not in nx_g.nodes():
# nx_g.add_node(dest)
# evolution.append(deepcopy(nx_g))
# nx_g.add_edges_from([(src, dest), (dest, src)])
# evolution.append(deepcopy(nx_g))
#
# def animate(i):
# ax.cla()
# g_t = evolution[i]
# nx.draw_circular(g_t, with_labels=True, ax=ax,
# node_color=['#FEBD69'] * g_t.num_nodes())
#
# fig, ax = plt.subplots()
# ani = animation.FuncAnimation(fig, animate,
# frames=len(evolution),
# interval=600)
#
# .. figure:: https://user-images.githubusercontent.com/19576924/48928548-2644d200-ef1b-11e8-8591-da93345382ad.gif
# :alt:
#
# DGMG: Optimization objective
# ------------------------------
# Similar to language modeling, DGMG trains the model with *behavior cloning*,
# or *teacher forcing*. Assume for each graph there exists a sequence of
# *oracle actions* :math:`a_{1},\cdots,a_{T}` that generates it. What the model
# does is to follow these actions, compute the joint probabilities of such
# action sequences, and maximize them.
#
# By chain rule, the probability of taking :math:`a_{1},\cdots,a_{T}` is:
#
# .. math::
#
# p(a_{1},\cdots, a_{T}) = p(a_{1})p(a_{2}|a_{1})\cdots p(a_{T}|a_{1},\cdots,a_{T-1}).\\
#
# The optimization objective is then simply the typical MLE loss:
#
# .. math::
#
# -\log p(a_{1},\cdots,a_{T})=-\sum_{t=1}^{T}\log p(a_{t}|a_{1},\cdots, a_{t-1}).\\
#
def forward_train(self, actions):
"""
- actions: list
- Contains a_1, ..., a_T described above
- self.prepare_for_train()
- Initializes self.action_step to be 0, which will get
incremented by 1 every time it is called.
- Initializes objects recording log p(a_t|a_1,...a_{t-1})
Returns
-------
- self.get_log_prob(): log p(a_1, ..., a_T)
"""
self.prepare_for_train()
stop = self.add_node_and_update(a=actions[self.action_step])
while not stop:
to_add_edge = self.add_edge_or_not(a=actions[self.action_step])
while to_add_edge:
self.choose_dest_and_update(a=actions[self.action_step])
to_add_edge = self.add_edge_or_not(a=actions[self.action_step])
stop = self.add_node_and_update(a=actions[self.action_step])
return self.get_log_prob()
#######################################################################################
# The key difference between ``forward_train`` and ``forward_inference`` is
# that the training process takes oracle actions as input and returns log
# probabilities for evaluating the loss.
#
# DGMG: The implementation
# --------------------------
# The ``DGMG`` class
# ``````````````````````````
# Below you can find the skeleton code for the model. You gradually
# fill in the details for each function.
#
import torch.nn as nn
class DGMGSkeleton(nn.Module):
def __init__(self, v_max):
"""
Parameters
----------
v_max: int
Max number of nodes considered
"""
super(DGMGSkeleton, self).__init__()
# Graph configuration
self.v_max = v_max
def add_node_and_update(self, a=None):
"""Decide if to add a new node.
If a new node should be added, update the graph."""
return NotImplementedError
def add_edge_or_not(self, a=None):
"""Decide if a new edge should be added."""
return NotImplementedError
def choose_dest_and_update(self, a=None):
"""Choose destination and connect it to the latest node.
Add edges for both directions and update the graph."""
return NotImplementedError
def forward_train(self, actions):
"""Forward at training time. It records the probability
of generating a ground truth graph following the actions."""
return NotImplementedError
def forward_inference(self):
"""Forward at inference time.
It generates graphs on the fly."""
return NotImplementedError
def forward(self, actions=None):
# The graph you will work on
self.g = dgl.DGLGraph()
# If there are some features for nodes and edges,
# zero tensors will be set for those of new nodes and edges.
self.g.set_n_initializer(dgl.frame.zero_initializer)
self.g.set_e_initializer(dgl.frame.zero_initializer)
if self.training:
return self.forward_train(actions=actions)
else:
return self.forward_inference()
#######################################################################################
# Encoding a dynamic graph
# ``````````````````````````
# All the actions generating a graph are sampled from probability
# distributions. In order to do that, you project the structured data,
# namely the graph, onto an Euclidean space. The challenge is that such
# process, called *embedding*, needs to be repeated as the graphs mutate.
#
# Graph embedding
# ''''''''''''''''''''''''''
# Let :math:`G=(V,E)` be an arbitrary graph. Each node :math:`v` has an
# embedding vector :math:`\textbf{h}_{v} \in \mathbb{R}^{n}`. Similarly,
# the graph has an embedding vector :math:`\textbf{h}_{G} \in \mathbb{R}^{k}`.
# Typically, :math:`k > n` since a graph contains more information than
# an individual node.
#
# The graph embedding is a weighted sum of node embeddings under a linear
# transformation:
#
# .. math::
#
# \textbf{h}_{G} =\sum_{v\in V}\text{Sigmoid}(g_m(\textbf{h}_{v}))f_{m}(\textbf{h}_{v}),\\
#
# The first term, :math:`\text{Sigmoid}(g_m(\textbf{h}_{v}))`, computes a
# gating function and can be thought of as how much the overall graph embedding
# attends on each node. The second term :math:`f_{m}:\mathbb{R}^{n}\rightarrow\mathbb{R}^{k}`
# maps the node embeddings to the space of graph embeddings.
#
# Implement graph embedding as a ``GraphEmbed`` class.
#
import torch
class GraphEmbed(nn.Module):
def __init__(self, node_hidden_size):
super(GraphEmbed, self).__init__()
# Setting from the paper
self.graph_hidden_size = 2 * node_hidden_size
# Embed graphs
self.node_gating = nn.Sequential(
nn.Linear(node_hidden_size, 1), nn.Sigmoid()
)
self.node_to_graph = nn.Linear(node_hidden_size, self.graph_hidden_size)
def forward(self, g):
if g.num_nodes() == 0:
return torch.zeros(1, self.graph_hidden_size)
else:
# Node features are stored as hv in ndata.
hvs = g.ndata["hv"]
return (self.node_gating(hvs) * self.node_to_graph(hvs)).sum(
0, keepdim=True
)
#######################################################################################
# Update node embeddings via graph propagation
# '''''''''''''''''''''''''''''''''''''''''''''
#
# The mechanism of updating node embeddings in DGMG is similar to that for
# graph convolutional networks. For a node :math:`v` in the graph, its
# neighbor :math:`u` sends a message to it with
#
# .. math::
#
# \textbf{m}_{u\rightarrow v}=\textbf{W}_{m}\text{concat}([\textbf{h}_{v}, \textbf{h}_{u}, \textbf{x}_{u, v}]) + \textbf{b}_{m},\\
#
# where :math:`\textbf{x}_{u,v}` is the embedding of the edge between
# :math:`u` and :math:`v`.
#
# After receiving messages from all its neighbors, :math:`v` summarizes them
# with a node activation vector
#
# .. math::
#
# \textbf{a}_{v} = \sum_{u: (u, v)\in E}\textbf{m}_{u\rightarrow v}\\
#
# and use this information to update its own feature:
#
# .. math::
#
# \textbf{h}'_{v} = \textbf{GRU}(\textbf{h}_{v}, \textbf{a}_{v}).\\
#
# Performing all the operations above once for all nodes synchronously is
# called one round of graph propagation. The more rounds of graph propagation
# you perform, the longer distance messages travel throughout the graph.
#
# With DGL, you implement graph propagation with ``g.update_all``.
# The message notation here can be a bit confusing. Researchers can refer
# to :math:`\textbf{m}_{u\rightarrow v}` as messages, however the message function
# below only passes :math:`\text{concat}([\textbf{h}_{u}, \textbf{x}_{u, v}])`.
# The operation :math:`\textbf{W}_{m}\text{concat}([\textbf{h}_{v}, \textbf{h}_{u}, \textbf{x}_{u, v}]) + \textbf{b}_{m}`
# is then performed across all edges at once for efficiency consideration.
#
from functools import partial
class GraphProp(nn.Module):
def __init__(self, num_prop_rounds, node_hidden_size):
super(GraphProp, self).__init__()
self.num_prop_rounds = num_prop_rounds
# Setting from the paper
self.node_activation_hidden_size = 2 * node_hidden_size
message_funcs = []
node_update_funcs = []
self.reduce_funcs = []
for t in range(num_prop_rounds):
# input being [hv, hu, xuv]
message_funcs.append(
nn.Linear(
2 * node_hidden_size + 1, self.node_activation_hidden_size
)
)
self.reduce_funcs.append(partial(self.dgmg_reduce, round=t))
node_update_funcs.append(
nn.GRUCell(self.node_activation_hidden_size, node_hidden_size)
)
self.message_funcs = nn.ModuleList(message_funcs)
self.node_update_funcs = nn.ModuleList(node_update_funcs)
def dgmg_msg(self, edges):
"""For an edge u->v, return concat([h_u, x_uv])"""
return {"m": torch.cat([edges.src["hv"], edges.data["he"]], dim=1)}
def dgmg_reduce(self, nodes, round):
hv_old = nodes.data["hv"]
m = nodes.mailbox["m"]
message = torch.cat(
[hv_old.unsqueeze(1).expand(-1, m.size(1), -1), m], dim=2
)
node_activation = (self.message_funcs[round](message)).sum(1)
return {"a": node_activation}
def forward(self, g):
if g.num_edges() > 0:
for t in range(self.num_prop_rounds):
g.update_all(
message_func=self.dgmg_msg, reduce_func=self.reduce_funcs[t]
)
g.ndata["hv"] = self.node_update_funcs[t](
g.ndata["a"], g.ndata["hv"]
)
#######################################################################################
# Actions
# ``````````````````````````
# All actions are sampled from distributions parameterized using neural networks
# and here they are in turn.
#
# Action 1: Add nodes
# ''''''''''''''''''''''''''
#
# Given the graph embedding vector :math:`\textbf{h}_{G}`, evaluate
#
# .. math::
#
# \text{Sigmoid}(\textbf{W}_{\text{add node}}\textbf{h}_{G}+b_{\text{add node}}),\\
#
# which is then used to parametrize a Bernoulli distribution for deciding whether
# to add a new node.
#
# If a new node is to be added, initialize its feature with
#
# .. math::
#
# \textbf{W}_{\text{init}}\text{concat}([\textbf{h}_{\text{init}} , \textbf{h}_{G}])+\textbf{b}_{\text{init}},\\
#
# where :math:`\textbf{h}_{\text{init}}` is a learnable embedding module for
# untyped nodes.
#
import torch.nn.functional as F
from torch.distributions import Bernoulli
def bernoulli_action_log_prob(logit, action):
"""Calculate the log p of an action with respect to a Bernoulli
distribution. Use logit rather than prob for numerical stability."""
if action == 0:
return F.logsigmoid(-logit)
else:
return F.logsigmoid(logit)
class AddNode(nn.Module):
def __init__(self, graph_embed_func, node_hidden_size):
super(AddNode, self).__init__()
self.graph_op = {"embed": graph_embed_func}
self.stop = 1
self.add_node = nn.Linear(graph_embed_func.graph_hidden_size, 1)
# If to add a node, initialize its hv
self.node_type_embed = nn.Embedding(1, node_hidden_size)
self.initialize_hv = nn.Linear(
node_hidden_size + graph_embed_func.graph_hidden_size,
node_hidden_size,
)
self.init_node_activation = torch.zeros(1, 2 * node_hidden_size)
def _initialize_node_repr(self, g, node_type, graph_embed):
"""Whenver a node is added, initialize its representation."""
num_nodes = g.num_nodes()
hv_init = self.initialize_hv(
torch.cat(
[
self.node_type_embed(torch.LongTensor([node_type])),
graph_embed,
],
dim=1,
)
)
g.nodes[num_nodes - 1].data["hv"] = hv_init
g.nodes[num_nodes - 1].data["a"] = self.init_node_activation
def prepare_training(self):
self.log_prob = []
def forward(self, g, action=None):
graph_embed = self.graph_op["embed"](g)
logit = self.add_node(graph_embed)
prob = torch.sigmoid(logit)
if not self.training:
action = Bernoulli(prob).sample().item()
stop = bool(action == self.stop)
if not stop:
g.add_nodes(1)
self._initialize_node_repr(g, action, graph_embed)
if self.training:
sample_log_prob = bernoulli_action_log_prob(logit, action)
self.log_prob.append(sample_log_prob)
return stop
#######################################################################################
# Action 2: Add edges
# ''''''''''''''''''''''''''
#
# Given the graph embedding vector :math:`\textbf{h}_{G}` and the node
# embedding vector :math:`\textbf{h}_{v}` for the latest node :math:`v`,
# you evaluate
#
# .. math::
#
# \text{Sigmoid}(\textbf{W}_{\text{add edge}}\text{concat}([\textbf{h}_{G}, \textbf{h}_{v}])+b_{\text{add edge}}),\\
#
# which is then used to parametrize a Bernoulli distribution for deciding
# whether to add a new edge starting from :math:`v`.
#
class AddEdge(nn.Module):
def __init__(self, graph_embed_func, node_hidden_size):
super(AddEdge, self).__init__()
self.graph_op = {"embed": graph_embed_func}
self.add_edge = nn.Linear(
graph_embed_func.graph_hidden_size + node_hidden_size, 1
)
def prepare_training(self):
self.log_prob = []
def forward(self, g, action=None):
graph_embed = self.graph_op["embed"](g)
src_embed = g.nodes[g.num_nodes() - 1].data["hv"]
logit = self.add_edge(torch.cat([graph_embed, src_embed], dim=1))
prob = torch.sigmoid(logit)
if self.training:
sample_log_prob = bernoulli_action_log_prob(logit, action)
self.log_prob.append(sample_log_prob)
else:
action = Bernoulli(prob).sample().item()
to_add_edge = bool(action == 0)
return to_add_edge
#######################################################################################
# Action 3: Choose a destination
# '''''''''''''''''''''''''''''''''
#
# When action 2 returns `True`, choose a destination for the
# latest node :math:`v`.
#
# For each possible destination :math:`u\in\{0, \cdots, v-1\}`, the
# probability of choosing it is given by
#
# .. math::
#
# \frac{\text{exp}(\textbf{W}_{\text{dest}}\text{concat}([\textbf{h}_{u}, \textbf{h}_{v}])+\textbf{b}_{\text{dest}})}{\sum_{i=0}^{v-1}\text{exp}(\textbf{W}_{\text{dest}}\text{concat}([\textbf{h}_{i}, \textbf{h}_{v}])+\textbf{b}_{\text{dest}})}\\
#
from torch.distributions import Categorical
class ChooseDestAndUpdate(nn.Module):
def __init__(self, graph_prop_func, node_hidden_size):
super(ChooseDestAndUpdate, self).__init__()
self.graph_op = {"prop": graph_prop_func}
self.choose_dest = nn.Linear(2 * node_hidden_size, 1)
def _initialize_edge_repr(self, g, src_list, dest_list):
# For untyped edges, only add 1 to indicate its existence.
# For multiple edge types, use a one-hot representation
# or an embedding module.
edge_repr = torch.ones(len(src_list), 1)
g.edges[src_list, dest_list].data["he"] = edge_repr
def prepare_training(self):
self.log_prob = []
def forward(self, g, dest):
src = g.num_nodes() - 1
possible_dests = range(src)
src_embed_expand = g.nodes[src].data["hv"].expand(src, -1)
possible_dests_embed = g.nodes[possible_dests].data["hv"]
dests_scores = self.choose_dest(
torch.cat([possible_dests_embed, src_embed_expand], dim=1)
).view(1, -1)
dests_probs = F.softmax(dests_scores, dim=1)
if not self.training:
dest = Categorical(dests_probs).sample().item()
if not g.has_edges_between(src, dest):
# For undirected graphs, add edges for both directions
# so that you can perform graph propagation.
src_list = [src, dest]
dest_list = [dest, src]
g.add_edges(src_list, dest_list)
self._initialize_edge_repr(g, src_list, dest_list)
self.graph_op["prop"](g)
if self.training:
if dests_probs.nelement() > 1:
self.log_prob.append(
F.log_softmax(dests_scores, dim=1)[:, dest : dest + 1]
)
#######################################################################################
# Putting it together
# ``````````````````````````
#
# You are now ready to have a complete implementation of the model class.
#
class DGMG(DGMGSkeleton):
def __init__(self, v_max, node_hidden_size, num_prop_rounds):
super(DGMG, self).__init__(v_max)
# Graph embedding module
self.graph_embed = GraphEmbed(node_hidden_size)
# Graph propagation module
self.graph_prop = GraphProp(num_prop_rounds, node_hidden_size)
# Actions
self.add_node_agent = AddNode(self.graph_embed, node_hidden_size)
self.add_edge_agent = AddEdge(self.graph_embed, node_hidden_size)
self.choose_dest_agent = ChooseDestAndUpdate(
self.graph_prop, node_hidden_size
)
# Forward functions
self.forward_train = partial(forward_train, self=self)
self.forward_inference = partial(forward_inference, self=self)
@property
def action_step(self):
old_step_count = self.step_count
self.step_count += 1
return old_step_count
def prepare_for_train(self):
self.step_count = 0
self.add_node_agent.prepare_training()
self.add_edge_agent.prepare_training()
self.choose_dest_agent.prepare_training()
def add_node_and_update(self, a=None):
"""Decide if to add a new node.
If a new node should be added, update the graph."""
return self.add_node_agent(self.g, a)
def add_edge_or_not(self, a=None):
"""Decide if a new edge should be added."""
return self.add_edge_agent(self.g, a)
def choose_dest_and_update(self, a=None):
"""Choose destination and connect it to the latest node.
Add edges for both directions and update the graph."""
self.choose_dest_agent(self.g, a)
def get_log_prob(self):
add_node_log_p = torch.cat(self.add_node_agent.log_prob).sum()
add_edge_log_p = torch.cat(self.add_edge_agent.log_prob).sum()
choose_dest_log_p = torch.cat(self.choose_dest_agent.log_prob).sum()
return add_node_log_p + add_edge_log_p + choose_dest_log_p
#######################################################################################
# Below is an animation where a graph is generated on the fly
# after every 10 batches of training for the first 400 batches. You
# can see how the model improves over time and begins generating cycles.
#
# .. figure:: https://user-images.githubusercontent.com/19576924/48929291-60fe3880-ef22-11e8-832a-fbe56656559a.gif
# :alt:
#
# For generative models, you can evaluate performance by checking the percentage
# of valid graphs among the graphs it generates on the fly.
import torch.utils.model_zoo as model_zoo
# Download a pre-trained model state dict for generating cycles with 10-20 nodes.
state_dict = model_zoo.load_url(
"https://data.dgl.ai/model/dgmg_cycles-5a0c40be.pth"
)
model = DGMG(v_max=20, node_hidden_size=16, num_prop_rounds=2)
model.load_state_dict(state_dict)
model.eval()
def is_valid(g):
# Check if g is a cycle having 10-20 nodes.
def _get_previous(i, v_max):
if i == 0:
return v_max
else:
return i - 1
def _get_next(i, v_max):
if i == v_max:
return 0
else:
return i + 1
size = g.num_nodes()
if size < 10 or size > 20:
return False
for node in range(size):
neighbors = g.successors(node)
if len(neighbors) != 2:
return False
if _get_previous(node, size - 1) not in neighbors:
return False
if _get_next(node, size - 1) not in neighbors:
return False
return True
num_valid = 0
for i in range(100):
g = model()
num_valid += is_valid(g)
del model
print("Among 100 graphs generated, {}% are valid.".format(num_valid))
#######################################################################################
# For the complete implementation, see the `DGL DGMG example
# <https://github.com/dmlc/dgl/tree/master/examples/pytorch/dgmg>`__.
#
tutorials/models/3_generative_model/README.txt
+14
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.. _tutorials3-index:
Generative models
--------------------
* **DGMG** `[paper] <https://arxiv.org/abs/1803.03324>`__ `[tutorial]
<3_generative_model/5_dgmg.html>`__ `[PyTorch code]
<https://github.com/dmlc/dgl/tree/master/examples/pytorch/dgmg>`__:
This model belongs to the family that deals with structural
generation. Deep generative models of graphs (DGMG) uses a state-machine approach.
It is also very challenging because, unlike Tree-LSTM, every
sample has a dynamic, probability-driven structure that is not available
before training. You can progressively leverage intra- and
inter-graph parallelism to steadily improve the performance.