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COMP9312 Data Analytics for Graphs
创建日期：2024-08-20 16:55:12
标签： COMP9312
Data Analytics for Graphs
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COMP9312 Data Analytics for Graphs
Assignment 2
Distributed Graph Processing, Feature Engineering,
and Graph Neural Networks
Important updates:
Fix the error or the weight matrix W and make the GAT layer
formulation clearer in Q2.1.
Summary
Submission Submit an electronic copy of all answers on Moodle
(Only the last submission will be used).
Required
Files
A .pdf file is accepted. The file name should be
ass2_zid.pdf
Deadline 9 pm Friday 2 August (Sydney Time)
Marks 20 marks (10% toward your total marks for this
course)
Late penalty. 5% of max assessment marks will be deducted for each
additional day (24 hours) after the specified submission time and date.
No submission is accepted 5 days (120 hours) after the deadline.
START OF QUESTIONS
Q1 (3 marks)

Figure 1
Figure 2 Figure 3
1.1 Are the graphs in Figure 1 and Figure 2 homomorphic? If so,
demonstrate a matching instance. (1 mark)
1.2 Present all unique subgraphs in Figure 1 that are isomorphic to the
graph in Figure 3. For example, { }, {
}, and { } are all considered as
the same subgraph 123. (2 marks)
Marking for Q1.1: 1 mark is given for the correct answer. 0 mark is
given for all other cases.
Marking for Q1.2: 2 marks are given if the result subgraphs are
correct, complete, and not redundant. Extra subgraphs and missing
subgraphs will result in a loss of marks.
Q2 (5 marks)
2.1 Given an undirected graph as shown in Figure 4,
Figure 4
we aim to compute the output of the first graph convolutional layer
with self-loops using the Graph Attention Network (GAT) model. The
goal is to transform the initial node embeddings from a dimension of 4
to a dimension of 5 through this layer. The equation can be written as:
v1 : 1, v2 : 2, v3 : 3
v1 : 2, v2 : 1, v3 : 3 v1 : 3, v2 : 1, v3 : 2
H 1

where indicates the -dimensional embedding of node in layer ,
and . is the
weighting factor of node 's message to node .
denotes the weight matrix for the neighbours of in layer , denotes
the dimension of the node embedding in layer . denotes the
non-linear function. The initial embedding for all nodes is
stacked in . is the weight matrices. Self-loops are included in
the calculation to ensure that the node's information is retained.
Therefore, the term is added to its set of neighbors, which can be
expressed as . Round the values to 2 decimal places (for
example, 3.333 will be rounded to 3.33 and 3.7571 will be rounded to
3.76). (3 marks)
2.2 Please determine whether the following statements are TRUE or
FALSE. (2 marks)
a. Skip-connections is a good technique used to alleviate over-
smoothing.
b. To design a model for predicting dropout on a course website, we
represent it as a bipartite graph where nodes indicate students or
courses. The task here is considered as node classification.
c. Graph Attention Network (GAT) has less expressive power
compared to GCN, as it computes the attention score between
each pair of neighbors, which introduces extra computational
complexity.
d. The main difference between GraphSAGE and GCN is that
GraphSAGE needs an activation function to add nonlinearity.
Marking for Q2.1: 3 marks are given for the correct result. Incorrect
values will result in a deduction of marks. Providing a detailed and
correct description of the calculation will earn marks for a valid
attempt, even if there are major mistakes in the result.
Marking for Q2.2: 0.5 mark is given for each correct TRUE/FALSE
answer.
Q3 (8 marks)
h(l)v =
u N(v) {v}
vuW (l)h
(l?1)
hlv dl v l
H l = [hlv1, h
l
v2, h
l
v3, h
l
v4, h
l
v5, h
l
v6]
T avu = 1|N(v) {v}|
u v W (l) Rdl?dl?1
v l dl
l (?)
ReLU
H 0 W 1
v
{v} N(v)
H 0 =

Figure 5
Suppose we aim to count the number of shortest paths from a source
vertex to all other vertices in an undirected unweighted graph shown
using Pregel.
3.1 Write the pseudocode for the compute implementation in Pregel. (3
marks)
3.2 Assume we run your algorithm with the source node 1 for the graph
in Figure 5 on three workers. Vertices 1 and 5 are in worker X. Vertices
2 and 4 are in worker Y. Vertices 3, 6 and 7 are in worker Z. Please
indicate the set of active vertices and how many messages are sent in
each iteration. (3 marks)
3.3 Can the combiner optimization be used in this case? If yes, write
the pseudocode for a combiner implementation. Calculate how many
messages are sent in each iteration if the combiner is used in 3.2. If no,
briefly discuss why a combiner cannot be used. (2 marks)
Marking for Q3.1: 3 marks are given for the correct answer. 0 mark is
given for all other cases.
Marking for Q3.2: 2 marks are given for the correct answer. 0 mark is
given for all other cases.
Marking for Q3.3: 3 marks are given for the correct answer. 0 mark is
given for all other cases.
Q4 (4 marks)
Consider the graph in Figure 6,

Figure 6
Figure 7
4.1 Compute the betweenness centrality and closeness centrality of
nodes C and H in Figure 6. Round the values to 2 decimal places (for
example, 3.333 will be rounded to 3.33 and 3.7571 will be rounded to
3.76). (2 marks)
4.2 Given the graphlets in Figure 7, derive the graphlet degree vector
(GDV) for nodes A and G. Note that only the induced matching
instances are considered in GDV. (2 marks)
Marking for Q4.1: 1 mark is given for correct betweenness centrality
values. 1 mark is given for correct closeness centrality values.
Marking for Q4.2: 1 mark is given for each correct vector. Incorrect
values in each vector will result in a deduction of marks.
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MATH20602 COMP532 MAS275 COMP5318 COMP4002 FIT5086 MAST20004 FIT3152 FIT5129 CIS2380 CS521 COMP 1005 EECMS CITS5501 ECE 462 ECON 6002 ENG 4051 CSC 648 CMT654 MECHENG 713 PHYS1002 AMME 2000 FP0060 DDES3200 MECHENG 743 BINF90002 FIT2081 ISYS90081 ELECTENG 722 BUS 360 ECOS3010 BUS2810 ETF2100 ENG2048 STAT5002 COMP2017 CEME 2003 MATS3004 COMP9319 PHYS1001 COMP5349 AMME2261 COMP-381 FIT3173 COSC2757 ENG4025 QBUS2820 COMP9414 MATH2021 EOSC118 MFIN6690 PMATH 321 CSE-141L MATH575A COMPSCI5002 COMP1511 management comp2123 FINS3616 COMP 3331 COMS30034 DTSC 71 AcF 702 AcF702 DTSC71 MAT021 ELE8083 ACFI213 EG-127J 127J FIT5163 FIT2001 ELE00113M CMT310 CS 245 ENGL 1101 MTH6115 EE497 CS 325 Math 124A MTH5130 MBA502 MGT 5380 ARCH 1261 F033800 20LLP109 ELE4009 FINANCIAL COMP3331 Computer ECE4179 20T3 COMP9311 COMP9311 UNSW MFIN6210 ACCT 5930 EE590 ENG2029 ECO100 SIT315 ACCT3610 COMP3600 STK2100 FIT2004 COMP30020 ACTL1101 Stat 101B BANA 200 COSC2473 ENGG1400 AI COMP90043 MMF 1914H PHYS 127 CS584 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MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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