Using the Design and Control Systemic Methodology to calculate Systems Complexity

Using the Design and Control Systemic Methodology to calculate Systems Complexity
Panagiotis Papaioannou
University of Piraeus
p.papaioannou@gmail.com
HSSS 9th
National & International Conference, 11-13 July 2013, Volos, Greece
This work deals with the systems or models complexity and proposes a method to measure the
complexity of a system designed using the Design and Control Systemic Methodology (DCSYM).
Although the term "complexity" appears more and more in our everyday conversations, it turns out
it is very difficult to define it. However, the majority of definitions relate the term complexity with
parts and relations between them, which leads to the concept of the system.
There are many reasons to deal with the complexity all based on the acceptance that we live in a
complex world. Almost all phenomena occur due to the interaction between lots of things, forming
systems, which result to the situations we face. To understand or to deal with them, we formulate
models that usually are abstraction of the reality, still capable to make us able to understand it
and/or to design effective interventions. These models are also systems and their complexity
relates either to the difficulty to deal with that systems or the value they expose to their
environment.
Since a system consists of parts and relations between them, the most proper equivalent is the
"graph" as defined in the graph theory. A graph consists of nodes (vertices) and lines (edges).
Lines act as links between nodes. DCSYM represents systems employing a specific notation. It
uses rectangles to represent systems or subsystems, circles to represent individuals and lines to
represent relations between them. A system can contain other subsystems or individuals. That
nesting acts as a hierarchy link between the container and the contained element. The whole
concept leads directly to a "graph" as described previously.
A method to measure the complexity of a graph is McCabe's "Cyclomatic Complexity". The
Cyclomatic Complexity (CC) of a graph is: CC = E - N + 2P
Where: P = number of disconnected parts of the graph
E = number of edges
N = number of nodes
In a system, there are no disconnected parts (in other case it would not be a system), thus, P=1.
After that, the definition of the Cyclomatic Complexity becomes: CC = E - N + 2.
To calculate the Cyclomatic Complexity of a system we use the above definition. N is the total
number of systems, subsystems and individuals. E is the total number of relations between all of
them. Note that every Edge counts once.
This approach assumes that all relations have the same weight. In actual situations, the meaning
of complexity relates also to the variety of a relation between two elements. To include this into the
measurement of the complexity we count each Edge (Relation) not only once but by a number
which expresses the variety (or difficulty) of this relation. We call the complexity calculated in this
way "Extended Cyclomatic Complexity".
An experimental software, titled DCSYM CASE TOOL, is used to design systems according to
DCSYM and includes the calculation of the complexity using the above two methods.

Using the Design and Control Systemic Methodology
to calculate Systems Complexity
Panagiotis Papaioannou
University of Piraeus
CSAP
HSSS 9th National & International Conference, 11-13 July 2013, Volos, Greece
2
DCSYM :: SYSTEMS COMPLEXITY
What is Complexity?
Neil Johnson (well known for his work on complexity)
• There is no unique definition of complexity
• It has traditionally been expressed using particular examples.
• Complexity Science: The study of the phenomena which emerge from
a collection of interacting objects
Definitions of complexity often depend on the concept of a “system”
(set of parts and relations between them)
The term “Complexity" appears more and more in our everyday
conversations, but it is very difficult to define it.

3
Disorganized Complexity vs. Organized Complexity
Examples
Gas in a container
Disorganized Organized
Departments – Processes - Relations
We are interested in Organized Complexity
4
A system or model more complex than another one:
• More difficult to understand it
• More difficult to manage it
• More expensive
• More risky
• Less predictable
Complexity is used in the context of Systems or Models
Why to measure Complexity
But may be:
• More accurate
• More adaptive
• … … ...

5
System: set of interacting or interdependent components forming an
integrated whole
B
F
D
A
E
C
Component
(Node)
Relation / Interaction
(Edge)
System: Definition and Representation
6
A system is a graph
We employ the concept of “graph complexity” to represent the
complexity of the system.
mathematical structure used to model pairwise relations between
objects
Graph:
Graph (from mathematics)

7
The Cyclomatic Complexity (CC) of a graph is:
CC = E - N + 2P
Where:
E = number of edges
N = number of nodes
P = number of disconnected parts of the graph
In a system, there are no disconnected parts
(in other case it would not be a system) P=1.
Cyclomatic Complexity of a System: SCC = E - N + 2.
What it expresses:
CC = 7 – 6 + 2 = 3
McCabe's Cyclomatic Complexity
The number of “cycles” made by the nodes-relations topology
(starting ending at the same node)
Used in Software Engineering but with without significant results.
8
DCSYM: Design Control SYstemic Methodology
A mean to design systems (models)
System-A
1s
System-B
2s
Subsystem
21s
Subsystem
22s
221i
Individual
4i
Individual
c
Communication
D
Control
g
Communication
U
Control

9
c, C communication
g, G general interaction or influence
u, U purposeful action
p, P potential conflict
d, D distorted communication
δ, Δ distorted purposeful communication
Communication Control
Bowen symbols
10
Link types:
• Relations
• Hierarchy Links
Hidden Links: Hierarchy Links

11
SCC = E - N + 2.
N is the total number of systems, subsystems and individuals.
E is the total number of relations between all of them
plus the number of hierarchy links (each relation/link counts once)
SCC = 6 – 5 + 2 = 3
System’s Cyclomatic Complexity ( SCC )
STOP!
It’s Good for
hard systems only!
12
Hard vs. Soft Systems
The system is well defined and deterministic.
Relations are fixed
Predictable behavior
Hard Systems:
The approach until now assumes that all relation are of the same quality.
This is good for Hard Systems.
The system is not well defined
Not deterministic (e.g. social systems)
Relations are not fixed:
• Variety
• Assumptions
• Noise
• Distortion
Soft Systems:
Complexity

13
To represent the quality of each relation
and the amount of complexity it accumulates
we use the concept of the Cost.
Relations are not of the same quality
Cost Interpretation
1 Hard relation (in a hard system)
2
Noise, Distortion, Uncertainty
Contribution to Systems’ Complexity
3
4
5 Higher
Lower
Complexity in Soft Systems
14
Step 0 Cyclomatic Complexity of a Graph: CC = E - N + 2P
E = Number of edges, N = Number of Nodes,
P = Number of disconnected graphs
Step 1 In a system: P=1 = CC = E – N + 2
E = Edges: Number of links (relations)
Step 2 + Hierarchy links E = Number of Relation Links
plus the number of Hierarchy Links.
Step 3 + Relations’ Contribution
to the complexity
E = Sum of Cost of the Relation Links
plus the number of Hierarchy Links
Review: Cyclomatic Complexity of a Soft System
Extended Systems Cyclomatic Complexity: ESCC = E - N + 2
E is the Sum of Costs of relations between all of them
plus the number of hierarchy links

15
Extended Systems Cyclomatic Complexity
ESCC = E - N + 2
E is the Sum of Costs of relations between all of them
plus the number of hierarchy links
16
A software to design systems and to calculate the extended cyclomatic complexity
DCSYM CASE TOOL

17
Examples
18

19
System0 System1
System2 System3
EXTENDED CYCLOMATIC COMPLEXITY: 4
Hard System
(1)
(1)
(1)
(1)
(1)
System6
System7
(1)
(1)
(1)
20

21
22
Panagiotis (Takis) Papaioannou

23
In order to control and survive:
• We reduce imported variety (making proper models)
• We create and export variety
Viable
System
(VS)
Management
(VM)
Complexity Attenuator
(Models)
Environment
(VE)
Complexity Amplifier
Example: Complexity awareness in the Viable System Model

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