Arrange networks

• Node-link diagrams: networks and trees

• Adjacency matrix: networks and trees• Enclosure: trees

Classification

Node-link diagrams• It is the most common technique for datasets based on networks and

trees.• Lines are used to represent the links that connect the items and

points to represent the elements of the dataset.• This type of representation uses connectivity based marks to

represent relationships between items.• The link density of a network is the ratio between the number of links

and the number of nodes.• Trees have a density of 1, with 1 link per node.• It is advisable not exceed density values of 3 or 4.

Node-link diagrams: trees

[Buchheim et al. 02]

[Bostock et al. 11]

Node-link diagrams: radial trees

Node-link diagrams: dense trees

[Auber et al. 12]

Node-link diagrams: dense trees

[Auber et al. 12]

Node-link diagrams: dense trees

[Auber et al. 12]

Node-link diagrams: trees• Three alternatives were presented to visually encode trees:

• Rectilinear vertical node-link diagrams, using connection marks to show the relationships between items, and using vertical space to show the depth of the tree and horizontal space to show the fraternal relations at a given level of the tree.

• Horizontal node-link diagrams, identical to the vertical but exchanging the horizontal and vertical spatial channels to represent respectively in this case the depth and the fraternal relations at a certain level of the tree.

• Radial node-link diagrams using connection markings to show relationships between items. The depth of the tree is represented in the radial direction and the angular position collects the fraternal relations at a given level of the tree.

Node-link diagrams: network topology• It is a technique of representation that is very well suited for tasks

that involve to understand the topology of a network.• Nodes that have a direct connection will be perceived as having a

closer relationship that the nodes that are connected through a sequence with multiple hops between nodes.

• The length of the path is a way to measure distances in a network, but while the distance in space is a continuous measure, in a network it is a discrete value.

• Connection marks can plot paths between nodes.• The size and color are common channels for encoding the nodes and

links.

Node-link diagrams: network topology tasks• You can pose the following tasks related to the topology of a network:

• Find all the possible paths between two nodes.• Find the shortest path between two nodes.• Given one node, find all the neighbors.• Find all the nodes that allow to stablish connections between two regions of

the network.

Node-link diagrams: node placement• These diagrams do not typically use spatial position to directly encode

attribute values.Algorithms to place the nodes are designed to minimize the number

of distractors, e.g. link intersections or nodes overlapping, so that the spatial position of the elements to encode the values of attributes is a side effect of such algorithms.

• Although it is relatively simple to extend this type of representation to 3D, it is not usually an effective solution and it is preferable to work only in 2D.

Node-link diagrams: examples[Gehlenborg y Wong 12]

Node-link diagrams: force-directed placement• One of the most used criteria to position the nodes of the network

that use connection marks is the use of forces of attraction and repulsion.

• One option is to use the repulsion force in the nodes and the attraction forces in the links, like springs.

• In a first step, such algorithms usually position randomly the nodes in a given spatial region, and then refine the positions of the items by simulating forces that push or pull them.

• The problem with these techniques is that some training is required to effectively analyze this visual encoding, because the spatial proximity of the nodes may be caused by the algorithm used rather than produced by the semantics of the data.

Node-link diagrams: force-directed placement• Another problem with these techniques is that they lead to non-

deterministic representations, so you can not take advantage of the spatial memory after successive executions.

• Furthermore, these techniques have scalability problems at both visual and algorithmic complexity.

• The simplest version of this approach fails to obtain a representation with a stable position, so in a context of multiple simultaneous views, it can become a distractor.

Node-link diagrams: force-directed placement

[Bostock et al. 11]

Node-link diagrams: force-directed placement

[Bostock et al. 11]

Node-link diagrams: multilevel approaches• To try to improve the scalability of such representations, multilevel

approaches arise, where the original network is transformed into a hierarchy of increasingly simpler versions that try to collect the essential characteristics of the original structure.

• Thus a graph composed is generated by combining the original network and the derived hierarchy of representations.

• Walking through the hierarchy from the simplest to the most complex representation improves both efficiency in the interpretation of the network and its rendering speed.

• Moreover, such approaches reduce the problem of falling into local minima in force-directed techniques.

Node-link diagrams: multilevel approaches[Hu 05]

Node-link diagrams: multilevel approaches[Hu 05]

Adjacency matrix• The network can be represented by a matrix deriving a table of the

original data.• In an adjacency matrix network nodes are distributed along the two

axes, horizontal and vertical, composing a rectangular region and the links between nodes are represented coloring a mark based on regions over the matrix cell that is the intersection of the corresponding row and column.

• The network has been transformed into a table with two keys, formed from the whole list of network nodes, and an attribute value for each cell that indicates whether there is link associated with the key values.

• You can add new attributes to the cells, often encoded with color or size.

• Undirected networks can be represented by triangular matrices.

Adjacency matrix [Gehlenborg y Wong 12]

Adjacency matrix

[McGuffin 12]

Node-link diagrams vs. adjacency matrix• Unlike force-directed diagrams, adjacency matrices are predictable –

taking into account the space required for representation - stable -the addition or deletion of items represent minor changes and usually local - and rearrangeable – considering that they can be performed interactively -.

• The stability of the adjacency matrix also allows both geometric and semantic zoom.

• The matrix representation also facilitates certain tasks:• Estimate the number of nodes.• Query information through node indexing.• Find patterns (once users are trained).

• The main problems that presents the adjacency matrix are the following:

• Users may not know.• Information about the network topology is derived indirectly, unlike diagrams

where it is displayed directly.• This is important because in most of the more complex tasks that may arise in

the various application domains that require exploration of a data set based on networks, it is required the topology analysis as a specific subtask.

• Hybrid solutions that combine both approaches can be a good solution to enhance the strengths in each case.

Node-link diagrams vs. adjacency matrix

Hybrid solution combining adjacency matrixand node-link diagrams

[Henry y Fekete 06]

Containment• Containment marks are very effective to represent the whole

information of a hierarchical structure, rather than just representing the relationships between pairs of items.

• They are typically used to represent compound structures such as trees, networks and graphs.

• In compounds graphs, the containment marks are often used to explore a derived hierarchy that collects clusters of nodes of the original graph.

• All of the children of a tree node are enclosed within the area allocated by that node, creating a nested layout.

• The size of the nodes is associated with values of some of the attributes of the items.

• Containment marks are not so effective as the connection marks for tasks oriented to the analysis of the topology of the structure, but they stand out in tasks related with the analysis of the values of the attributes in the leaves.

• They are typically used when hierarchical representations are much wider than deep.

Containment: treemap

Containment: treemap

[Auber et al. 12]

Containment: compound graphs

[Archambault et al. 08]

Comparison of representations

[McGuffin and Robert 10]

References• Tamara Munzner. Visualization Analysis and Design. A K Peters

Visualization Series. CRC Press. Oct 2014.• [Buchheim et al. 02] Christoph Buchheim et al. “Improving Walker's

Algorithm to Run in Linear Time” In Proc. Graph Drawing (GD'02), pp. 344-353, Springer LNCS, 2002

• [Bostock et al. 11]: Michael Bostock et al. “D3: Data-Driven Documents” IEEE Trans. Visualization and Computer Graphics. 17(12): 2301-2309, 2011.

• [Auber et al. 12] David Auber et al. “The Tulip 3 Framework: A Scalable Software Library for Information Visualization Applications Based on Relational Data." Technical report, INRIA Research Report 7860, 2012.

• [Hu 05] Yifan Hu. “Efficient and high quality force-directed graph drawing”, The Mathematica Journal 10 (2005), 37-71. yifanhu.net/GALLERY/GRAPHS/

References• [Gehlenborg y Wong 12] Nils Gehlenborg y Bang Wong, “Points of

view: Networks” Nature Methods 9:115.• [McGuffin 12] Michael J. McGuffin, “Simple Algorithms for Network

Visualization: A Tutorial” Tsinghua Science and Technology 17(4): 383-398, 2012.

• [Henry y Fekete 06]: Nathalie Henry and Jean-Daniel Fekete“MatrixExplorer: a Dual-Representation System to Explore Social Networks” IEEE Trans. Visualization and Computer Graphics. 12(5): 677-684, 2006.

• [McGuffin and Robert 10] Michael J. McGuffin and Jean-Marc Robert “Quantifying the Space-Efficiency of 2D Graphical Representations of Trees” Information Visualization 9(2): 115-140, 2010.

• [Archambault et al. 08] Dan Archambault et al. ”GrouseFlocks: Steerable Exploration of Graph Hierarchy Space” IEEE Trans. on Visualization and Computer Graphics 14(4): 900-913, 2008.

Node-link diagrams: examples[Gehlenborg y Wong 12]

Node-link diagrams: dense trees

[Auber et al. 12]