Network Data Models

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Network Data Models

• Talbot J. Brooks
• (Additional input from Dr. Wentz ASU Geography
  and Dr. Gunter Krumme, University of Washington)
• ASU Dept. of Geography

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Overview of topics in this module

• Basic networks and demonstration (Today)
• Networks lab (Wednesday)
• Linear referencing (Monday)
• Dynamic segmentation (next Wednesday)

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What is a Network?

• Networks are special types of topologic feature
  models composed of nodes (points) and links
  (lines).
• Topology is modified with impedance to flow
  (resistance)
• Impedance may be imposed at either/both nodes and
  lines

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Two fundamental types

• There are two basic types of networks
• Radial (sometimes called tree networks) always
  have upstream or downstream flow. River systems
  are an example of radial networks
• Looped networks are characterized by
  self-intersections and do not have a defined
  upstream or downstream. Water and power
  distribution systems as example of looped
  networks.

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Other types/variants of networks

• Straight network (animal movement)
• Branching network (stream patterns)
• Circuit (street patterns)
• Directed flows can move in a single direction
• Undirected flows can move in either direction

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Networks are specific

• Networks operate under specific conditions that
  are unique to the system being modeled. These
  conditions determine which network model is
  required.
• Sewer systems are one directional and must flow
  downhill (there are some exceptions to the
  latter) must use a radial model
• Communications systems have complex routing rules
  and may not always connect 2 parties via the same
  path and have multiple self-intersections must
  use a looped model

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A simple example

• A group of streets may be considered a network
• Intersections are nodes. They become weighted if
  a traffic control device is in place.
• Streets are links. They connect nodes and may
  have directly imposed weights such as speed
  limits or implied weights such as road surface
  type or number of lanes.
• Network topologic relationships define how lines
  connect with each other at nodes

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Some Terms

• Edges (links) Streets, transmission lines, pipe,
  and stream
• Junctions (nodes) Street intersections, fuses,
  switches, service taps, and the confluence of
  stream reaches are examples of junctions
• Impedance the cost associated with traveling
  along a specific link

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Edges and junctions

• Edges and junctions can be either simple or
  complex. Simple network features correspond to a
  single network element in the network. A complex
  network feature corresponds to more than one
  network element in the network.

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Simple edges and junctions

• Simple edges are always connected to exactly two
  junction features, one at each end.

Simple junction
Simple edge
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Complex edges

• Complex edges are always connected to at least
  two junction features at their endpoints but can
  be connected to additional junction features
  along their length.

Here we have a water pipe that is Split. This is
common in many house- Hold plumbing schemes.
There is no Valve between the split. The pipe is
a Complex edge.
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Complex junctions

• A junction where there is more than one
  connection.

Complex junction
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• Connectivity is an attribute of a network that
  measures the effort (minimum number of links)
  needed to reach all nodes from all other nodes
• Accessibility is an attribute of a node that
  measures the effort needed to reach all or
  certain nodes from a specific node
• Path is a set of consecutive links involving
  different nodes
• Fundamental circuits are closed paths which do
  not contain other circuits (such loops would be
  redundant)

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A Basic Connectivity Matrix
Network (Graph)
Network Diameter 4
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Connectivity Matrix (C)
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Analysis of networks

• Connectivity
• gamma index ratio between the number of links in
  a network to the maximum possible
• alpha index ratio of the number of routes
  through a network to the maximum possible
• Beta index compares the number of links with the
  number of nodes in a network (is a measure of
  complexity)
• Shortest path

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More analysis tools

• Associated number (Koenig Number) measures the
  accessibility (or centrality) of a node by the
  number of links needed to connect this node with
  the (topologically) most distant node in the
  network
• Shimbel Index is a measure of the minimum number
  of links necessary to connect one node with all
  nodes in the network

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• The diameter of a network is the number of links
  in the shortest path between the furthest pair of
  nodes. It is needed to identify the number of
  matric multiplications (using the adjacency
  matrix)
• Nodal degree is the sum of the direct links which
  connect a node to adjacent nodes. It can be
  calculated by summing rows or columns of direct
  connection matrix and is limited because it does
  not consider indirect links

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Gamma index
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Gamma Index
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Algorithm Terms

• Nodes
• Origin node
• Adjacent node
• Reached node
• Scanned node
• Unscanned node

• Cumulative Cost
• Tables
• Scanned table
• Reached table Cumulative Cost

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Step One
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Step Two
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Step Three
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Step Four
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Step Five
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Step Six
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Step Seven
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Step Eight
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Step Nine
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Step Ten
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Step Eleven
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Step Twelve
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Step Thirteen
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Introduction to networks in ArcGIS
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Enabled and disabled features

• In order for features to participate in a
  network, they must be enabled.
• A feature that is disabled in the network acts as
  a barrier.
• Construction on a street will stop traffic. That
  segment of the street has been disabled.
• When the network is traced, the trace will stop
  at any barriers it encounters in the network
  including disabled network features.
• The enabled or disabled state of a network
  feature is a property maintained by an attribute
  field called Enabled. It can have one of two
  values true or false.

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Flags

• Flags define the starting points for traces. For
  example, if you are performing a trace, you can
  use a flag to specify where the trace will begin.
  Place a flag at your house and one at work. Trace
  the path between these two places. Flags can be
  placed anywhere along edges or on junctions.

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Barriers

• If you are only interested in tracing on a
  particular part of your network, you can use
  barriers to isolate that part of the network.
• Like flags, barriers can be placed anywhere along
  edges or on junctions.
• When performing trace operations, ArcMap treats
  the network features with barriers as if they are
  disabled, thus preventing the trace from
  continuing beyond these features.
• Its just like a detour because of construction
  or an accident.

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Network operations

• Tracing is the primary analysis function you will
  perform. There are several functions you can do
• Adding flags and barriers
• Tracing upstream
• Tracing downstream
• Finding the upstream accumulation
• Finding an upstream path to the source
• Finding common ancestors
• Finding connected features
• Finding disconnected features
• Isolating a point on the network
• Finding connected features using weight filters
• Finding a path
• Finding the shortest path
• Finding an upstream path
• Finding loops

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Creating geometric networks

• As always, GN are created in ArcCatalog.
• They are created inside a feature dataset within
  a GDB. Not all feature classes within a feature
  dataset need to participate in a geometric
  network. A feature class however, can participate
  in only one GN.
• Uses a wizard that will request information about
  weights, tolerances, etc

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Creating geometric networks
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Replacement Exercise

• Determine how ArcGIS solves for the shortest path
  for any given street network that you create if
  weights are not assigned.
• Submit a brief explanation by next Monday.