MDA104 Introduction to Databases
2. Entity-Relationship Model
Vlastislav Dohnal
Credits
◼ Slides are part of the database bible:
 Database System Concepts, Seventh Edition. Avi
Silberschatz, Henry F. Korth, S. Sudarshan.
 https://db-book.com/
◼ Experience from courses of Faculty of
Informatics, Masaryk University
 PB168 - Fundamentals of Database and Information
Systems
 PB154 - Fundamentals of Database Systems
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Entity-Relationship Model
Modeling
E-R Diagram
Entity Sets and Relationships
Weak Entity Sets
Extended E-R Features
Design of the Bank Database
UML
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Entity-Relationship model
◼ Conceptual model used in the development of IS
 During requirements analysis
 Models information stored in the DB
◼ Easy to understand
 The customer "understands" it
Example – Loan in a bank
◼ Requirements
 A client applies for a loan
◼ purpose, how much, information about the client
 The bank approves the loan
◼ Decision
 What is data and what are processes?
◼ ERD for data
◼ DFD (Data-flow diagram) for processes
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DFD – Loan in a bank
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customer
Receipt
loan
req.
Process
loan
req.
Check
status
Loan application
Loanapplication
Confirmation
manager
Loans
History report
ERD – Loan in a bank
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approved
description
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Modeling
A database can be modeled as:
a collection of entities,
relationship among entities.
An entity is an object that exists and is distinguishable from other
objects.
Also, an entity must be “remembered”
Example: specific person, company, plant, event, product, invoice
Entities have attributes
Example: person has a name and address
An entity set is a set of entities of the same type that share the same
properties.
Example: set of all persons, companies, trees, holidays
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Entity Sets customer and loan
customer loan
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Relationship Sets
A relationship is an association among several entities
Example:
Hayes borrower A-102
customer entity relationship set loan entity
A relationship set is a mathematical relation among n  2 entities, each
taken from corresponding entity sets
R = {(e1, e2, … en) | e1  E1, e2  E2, …, en  En}
where (e1, e2, …, en) is a relationship
Example:
(Hayes, A-102)  borrower
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Relationship Set borrower
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Relationship Sets (Cont.)
An attribute can also be property of a relationship set.
For instance, the borrower relationship set between entity sets customer
and loan may have the attribute approval_reception_date
loan(loan_number)
borrower(approval_reception_date)
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Degree of a Relationship Set
Refers to the number of entity sets that participate in a relationship set.
Relationship sets that involve two entity sets are binary
Degree = two
Generally, most relationship sets in a database system are binary.
Relationship sets may involve more than two entity sets.
Example:
Suppose employees of a bank may have jobs (responsibilities)
at multiple branches, with different jobs at different branches.
Then there is a ternary relationship set between entity sets
employee, job, and branch
Relationships between more than two entity sets are rare.
Again, most relationships are binary. (More on this later.)
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Mapping Cardinality Constraints
Express the number of entities to which another entity can be
associated via a relationship set.
Most useful in describing binary relationship sets.
For a binary relationship set the mapping cardinality must be one of
the following types:
One to one
One to many
Many to one
Many to many
Mind that cardinality itself does not enforce the existence of a
“mapping”, i.e., a customer may not have any loan.
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Mapping Cardinalities
One to one One to many
Note: Some elements in A and B may not be mapped to any
elements in the other set
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Mapping Cardinalities
Many to one Many to many
Note: Some elements in A and B may not be mapped to any
elements in the other set
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Attributes
An entity is represented by a set of attributes
= descriptive properties possessed by all members of an entity set.
Name – each attribute has its name unique within an entity
Domain – the set of permitted values for each attribute
Attribute type
Simple attribute – single value
Composite attribute – single value but structured
Multi-valued attribute – multiple values, can repeat
Example: phone_numbers
Derived attribute
Can be computed from other entity’s attributes
Example: age, given date_of_birth
Example:
customer = (customer_id, customer_name, customer_street, customer_city )
loan = (loan_number, amount )
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Composite Attributes
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E-R Diagrams
Rectangles represent entity sets.
Diamonds represent relationship sets.
Ellipses represent attributes
Lines link attributes to entity sets and entity sets to relationship sets.
Attributes:
Double ellipses represent multivalued attributes.
Dashed ellipses denote derived attributes.
Underline indicates primary key attributes (will study later)
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E-R Diagram With Composite, Multivalued, and Derived Attributes
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Relationship Sets with Attributes
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Mapping Cardinality Constraints
We express cardinality constraints by drawing either
a directed line (→), signifying “one,” or
an undirected line (—), signifying “many,” between the relationship
set and the entity set.
One-to-one relationship:
A customer is associated with at most one loan via the relationship
borrower
A loan is associated with at most one customer via borrower
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One-To-Many Relationship
In the one-to-many relationship a loan is associated with at most one
customer via borrower, a customer is associated with several (including
zero) loans via borrower
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Many-To-One Relationships
In a many-to-one relationship, a loan is associated with several
(including zero) customers via borrower, a customer is associated with
at most one loan via borrower
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Many-To-Many Relationship
A customer is associated with several (possibly zero) loans via
borrower
A loan is associated with several (possibly zero) customers via
borrower
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Mapping Cardinalities affect ER Design
Especially, attributes of relationships
Can make access-date an attribute of account, instead of a relationship
attribute, if each account can have only one customer
That is, the relationship from account to customer is many to one, or
equivalently, customer to account is one to many
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Keys
Key = a subset of attributes of “special” interest
Search key
“Database / identification / unique” key
Referencing an entity
“Database key” (primary key constraint)
Defined for unique identification of each entity and/or relationship
A super key of an entity set is a set of one or more attributes whose
values uniquely determine each entity.
A candidate key of an entity set is a minimal super key
customer_id is a candidate key of customer
account_number is a candidate key of account
Although several candidate keys may exist, one of the candidate keys is
selected to be the primary key.
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Keys for Relationship Sets
The combination of primary keys of the participating entity sets forms a
super key of a relationship set.
(customer_id, account_number) is the super key of depositor
NOTE: this means a pair of entities can have at most one
relationship in a particular relationship set.
Example: if we wish to track all access_dates to each account by
each customer, we cannot assume a relationship for each
access. We may use a multivalued attribute.
Must consider the mapping cardinality of the relationship set when
deciding what the candidate keys are
Need to consider semantics of relationship set in selecting the primary
key in case of more than one candidate key
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E-R Diagram with a Ternary Relationship
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Cardinality Constraints on Ternary Relationship
We allow at most one arrow out of a ternary (or greater degree) relationship
to indicate a cardinality constraint
E.g., an arrow from works_on to job indicates an employee works at a
branch on at most one job.
If there is more than one arrow, there are two ways of defining the meaning.
E.g a ternary relationship R between A, B and C with arrows to B and C
could mean
1. each A entity is associated with a unique entity from B and C or
2. each pair of entities from (A, B) is associated with a unique C entity,
and each pair (A, C) is associated with a unique B
Each alternative has been used in different formalisms
To avoid confusion, we outlaw more than one arrow
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Roles
Entity sets of a relationship need not be distinct
The labels “manager” and “worker” are called roles; they specify how
employee entities interact via the works_for relationship set.
Roles are indicated in E-R diagrams by labeling the lines that connect
diamonds to rectangles.
Role labels are optional, and are used to clarify semantics of the
relationship
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Participation of an Entity Set in a Relationship Set
Total participation (indicated by double line)
every entity in the entity set participates in at least one relationship
in the relationship set
E.g., participation of loan in borrower is total
every loan must have a customer associated to it via borrower
Partial participation (default)
some entities may not participate in any relationship in the
relationship set
Example: participation of customer in borrower is partial
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Existence Dependencies
If the existence of entity x depends on the existence of entity y, then x
is said to be existence dependent on y.
y is a dominant entity (in example below, loan)
x is a subordinate entity (in example below, payment)
If a loan entity is deleted, then all its associated payment entities must
also be deleted.
loan-payment paymentloan
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Weak Entity Sets
Models the existence dependency
The existence of a weak entity set depends on the existence of an
identifying entity set
it must relate to the identifying entity set via a total
one-to-many relationship set from the identifying to the weak set
Identifying relationship depicted using a double diamond
Keys:
An entity set that does not have a primary key is referred to as a
weak entity set.
The discriminator (or partial key) of a weak entity set is the key that
distinguishes among all the weak entities corresponding to a specific
identifying entity.
The primary key of a weak entity set is formed by
the primary key of the strong entity set on which the weak entity
set is existence dependent,
plus, the weak entity set’s discriminator.
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Weak Entity Sets (Cont.)
We depict a weak entity set by double rectangles.
We underline the discriminator of a weak entity set with a dashed line.
payment_number – discriminator of the payment entity set
So, it can represent the order of individual payments of a loan.
Primary key for payment is (loan_number, payment_number)
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Weak Entity Sets (Cont.)
Note: the primary key of the strong entity set is not explicitly added to
the weak entity set, since it is implicit via the identifying relationship.
If loan_number was explicitly stored, payment could be made a strong
entity,
but then the relationship between payment and loan would be
duplicated by an implicit relationship defined by the attribute
loan_number common to payment and loan
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More Weak Entity Set Examples
In a university, a course is a strong entity and a course_offering can be
modeled as a weak entity
The discriminator of course_offering would be semester (including
year) and section_number (if there is more than one section)
If we model course_offering as a strong entity we would model
course_number as an attribute.
Then the relationship with course would be implicit in the
course_number attribute.
course course_offering
course_id
title
credits semester
section_number
time_schedule
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Design Issues
Use of entity sets vs. attributes
Choice mainly depends on the structure of the enterprise being
modeled, and on the semantics associated with the attribute in
question.
Use of entity sets vs. relationship sets
Possible guideline is to designate a relationship set to describe an
action that occurs between entities
Binary versus n-ary relationship sets
Although it is possible to replace any nonbinary (n-ary, for n > 2)
relationship set by a number of distinct binary relationship sets, an
n-ary relationship set shows more clearly that several entities
participate in a single relationship.
Placement of relationship attributes
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Binary Vs. Non-Binary Relationships
Some relationships that appear to be non-binary may be better
represented using binary relationships
E.g. A ternary relationship parents, relating a child to his/her
father and mother, is best replaced by two binary relationships,
father and mother
Using two binary relationships allows partial information (e.g.
only mother being know)
But there are some relationships that are naturally non-binary
Example: works_on
father
parents
mother
child
father
parent
child
mother
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Converting Non-Binary Relationships to Binary Form
In general, any non-binary relationship can be represented using
binary relationships by creating an artificial entity set.
Replace R between entity sets A, B and C by an entity set E, and
three relationship sets:
1. RA, relating E and A 3. RC, relating E and C
2. RB, relating E and B
Create a special identifying attribute for E
Add any attributes of R to E
For each relationship (ai , bi , ci) in R, create
1. a new entity ei in the entity set E 3. add (ei , bi ) to RB
2. add (ei , ai ) to RA 4. add (ei , ci ) to RC
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Converting Non-Binary Relationships (Cont.)
Also need to translate constraints
Translating all constraints may not be possible
There may be instances in the translated schema that
cannot correspond to any instance of R
Exercise:
Add constraints to the relationships RA, RB and RC to
ensure that a newly created entity (ei) corresponds to
exactly one entity in each of entity sets A, B and C
We can avoid creating an identifying attribute by making E a weak
entity set (described shortly) identified by the three relationship
sets
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Extended E-R Features: Specialization
A top-down design process
We designate subgroupings within an entity set that are distinctive
from other entities in the set.
These subgroupings become lower-level entity sets
can have attributes or participate in relationships
but do not apply to the higher-level entity set.
Depicted by a triangle component labeled ISA
E.g., customer “is a” person.
Inheritance
a lower-level entity set inherits all the attributes and
relationship participation of the higher-level entity set to which it is
linked.
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Specialization Example
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Extended ER Features: Generalization
A bottom-up design process
combine a number of entity sets that share the same features
into a higher-level entity set.
Specialization and generalization are simple inversions of each
other
they are represented in an E-R diagram in the same way.
The terms specialization and generalization are used
interchangeably.
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Specialization and Generalization (Cont.)
Can have multiple specializations of an entity set based on different
features.
E.g., permanent_employee vs. temporary_employee,
in addition to officer vs. secretary vs. teller
Each particular employee would be
a member of one of permanent_employee or
temporary_employee,
and also a member of one of officer, secretary, or teller
The ISA relationship also referred to as superclass - subclass
relationship
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Design Constraints on a Specialization/Generalization
Constraint on which entities can be members of a given lower-level
entity set.
condition-defined
Example: all customers over 65 years are members of seniorcitizen
entity set; senior-citizen ISA person.
user-defined
Constraint on whether or not entities may belong to more than one
lower-level entity set within a single generalization.
Disjoint
an entity can belong to only one lower-level entity set
Noted in E-R diagram by writing disjoint next to the ISA triangle
Overlapping
an entity can belong to more than one lower-level entity set
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Design Constraints on a Specialization/Generalization (Cont.)
Completeness constraint -- specifies whether or not an entity in the
higher-level entity set must belong to at least one of the lower-level
entity sets within a generalization.
Total: an entity must belong to one of the lower-level entity sets
Partial: an entity need not belong to one of the lower-level entity
sets
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Aggregation
Consider the ternary relationship works_on, which we saw earlier
Suppose we want to record managers for some tasks performed by an
employee at a branch
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Aggregation (Cont.)
Relationship sets works_on and manages represent overlapping
information
Every manages relationship corresponds to a works_on
relationship
However, some works_on relationships may not correspond to
any manages relationships
So we can’t discard the works_on relationship
Eliminate this redundancy via aggregation
Treat a relationship as an abstract entity
Allows relationships between relationships
Abstraction of relationship into new entity
Without introducing redundancy, the following diagram represents:
An employee works on a particular job at a particular branch
An employee, branch, job combination may have an associated
manager
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E-R Diagram With Aggregation
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E-R Design Decisions
Already discussed:
The use of an attribute or entity set to represent an object.
Whether a real-world concept is best expressed by an entity set
or a relationship set.
The use of a ternary relationship versus a set of binary
relationships.
The use of a strong or weak entity set.
The use of specialization/generalization
contributes to modularity in the design.
The use of aggregation
can treat the aggregate entity sets as a single unit without
concern for the details of its internal structure.
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E-R Diagram for a Banking Enterprise
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Summary of Symbols Used in E-R Notation
Chen’s E-R Notation
Cardinality limits can also express participation constraints
However, the other way around
It resembles Min-Max/ISO notation
This example expresses one-to-many relationship between
customer (one) and loan (many)
Moreover, each loan must have a customer assigned (total
participation)
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Alternative Notation for Cardinality Limits
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Alternative E-R Notations
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UML
UML: Unified Modeling Language
UML has many components to graphically model different aspects of an
entire software system
Supported techniques
data modeling (entity relationship diagrams)
business modeling (work flows)
object modeling
component modeling
UML Class Diagrams correspond to E-R Diagram
but there are several differences.
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Summary of UML Class Diagram Notation
Chen’s notation UML notation
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UML Class Diagrams (Cont.)
Entity sets are shown as boxes
attributes are shown within the box,
rather than as separate ellipses in E-R diagrams.
Binary relationship sets are represented in UML by just drawing a line
connecting the entity sets.
The relationship set name is written adjacent to the line.
The role played by an entity set in a relationship set may also be
specified by writing the role name on the line, adjacent to the entity set.
The relationship set name may alternatively be written in a box, along
with attributes of the relationship set
the box is connected, using a dotted line, to the line depicting the
relationship set.
Non-binary relationships drawn using diamonds
just as in ER diagrams
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UML Class Diagram Notation (Cont.)
* Note the reversal notation of numeric relationship cardinality constraints in UML
* Generalization can use merged or separate arrows independent of disjoint/overlapping
overlapping
disjoint
Chen’s notation UML notation
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UML Class Diagrams (Cont.)
Cardinality constraints are specified in the form l..h
l denotes the minimum and h the maximum number of
relationships an entity can participate in.
Beware: the positioning of the numeric constraints is exactly the
reverse of the positioning of them in E-R diagrams (with numeric
constraints).
But it is the same in case of arrows denoting 0..1.
The constraint 0..* on the E2 side and 0..1 on the E1 side means
that each E2 entity can participate in at most one relationship,
whereas each E1 entity can participate in many relationships;
in other words, the relationship is many to one from E2 to E1.
Single values, such as 1 or * may be written on edges;
The single value 1 on an edge is treated as equivalent to 1..1,
while * is equivalent to 0..*.
Takeaways
Differences between ERD and DFD
Create ERD from specification
Use the correct notation
Respect the rules of notation
do not forget the cardinality of the relationship
Different notations
connection to UML
Design decision rules
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