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COMPSCI 752

Big data management

Assignment 2 / Semester 1, 2023

Graph Databases

Model Answers

Graph databases

Consider a simple application where direct ﬂights between two cities are stored as a property graph. Nodes and edges may have properties.

Fig. 1. Property Graph

Questions:

1. Write down the formal property graph model (V, E, n, A, u) for the property graph in Figure 1. [6 marks]

Solution:

– V = {1, 2, 3}

– E = {10, 11}

– n:

. 10 →l (1, 2), 11 →l (2, 3)

– A:

. 1 → {city}, 2 → {city}, 3 → {city},

. 10 → {ﬂight}, 11 → {ﬂight}

– u:

. (1, name) → “Papeete”, (1, country) → “France”

. (2, name) → “Los Angeles”, (2, country) → “USA”,

. (3, name) → “Paris”, (3, country) → “France”,

. (10, airline) → “Air Tahiti”, (10, no) → “TN 8”,

. (11, airline) → “Air Tahiti”, (11, no) → “TN 8”,

2. Write the following English language query in regular property graph logic

Return all city nodes that can be reached from the city of Papeete with a sequence of connecting ﬂights with at most two stop-overs. [4 marks]

Solution:

result(3) - :ﬂight(y, 3), y.name = “Papeete”

result(3) - :ﬂight(y, z1), :ﬂight(z1, 3), y.name = “Papeete”

result(3) - :ﬂight(y, z1), :ﬂight(z1, z2), :ﬂight(z2, 3), y.name = “Papeete”

3. Write the following English language query in regular property graph logic

Return all city nodes that can be reached from the city of Papeete with a sequence of connecting ﬂights that have an unlimited number of stop-overs. [4 marks]

Solution:

result(·) - :ﬂight(y, 3), :ﬂight* (3, ·), y.name = “Papeete”

4. Write the following English language query in regular property graph logic

Return all city nodes in France, with a name diﬀerent from Papeete, that can be reached from the city of Papeete with a sequence of connecting ﬂights that have an unlimited number of stop-overs, where each ﬂight is international and operated by the airline “Air Tahiti” . [4 marks]

Solution:

reach(3, ·) - :ﬂight(3, ·) as k, k .airline = “Air Tahiti”, 3 .country · .country