The graphBAM class has been created as a more efficient
replacement for the graphAM class in the graph
package. The adjacency matrix in the graphBAM class is
represented as a bit array using a raw vector. This
significantly reduces the memory occupied by graphs having a large
number of nodes. The bit vector representation also provides advantages
in terms of performing operations such as intersection or union of
graphs.
We first load the graph package which provides the class definition and methods for the graphBAM class.
One of the arguments df to the graphBAM
constructor is a data.frame containing three columns:
“from”,“to” and “weight”, each row in the data.frame
representing an edge in the graph. The from and
to columns can be character vectors or factors, while the
weight column must be a numeric vector. The argument
nodes are calculated from the unique names in the
from and to columns of the
data.frame. The argument edgeMode should be a
character vector, either “directed” or “undirected” indicating whether
the graph represented should be directed or undirected respectively.
We proceed to represent a simple graph using the graphBAM
class. Our example is a directed graph representing airlines flying
between different cities. In this example, cities represent the nodes of
the graph and each edge represents a flight from an originating city
(from) to the destination city (to). The
weight represents the fare for flying between the from and
to cities.
df <- data.frame(from = c("SEA", "SFO", "SEA", "LAX", "SEA"),
to = c("SFO", "LAX", "LAX", "SEA", "DEN"),
weight = c( 90, 96, 124, 115, 259),
stringsAsFactors = TRUE)
g <- graphBAM(df, edgemode = "directed")
g## A graphBAM graph with directed edges
## Number of Nodes = 4
## Number of Edges = 5The cities (nodes) included in our graph object as well as
the stored fares(weight) can be obtained using the
nodes and edgeWeights methods
respectively.
## [1] "DEN" "LAX" "SEA" "SFO"## $SEA
## DEN LAX SFO
## 259 124 90
##
## $LAX
## SEA
## 115Additional nodes or edges can be added to our graph using the
addNode and addEdge methods. For our example,
we first add a new city “IAH” to our graph. We then add a flight
connection between “DEN” and “IAH” having a fare of $120.
## A graphBAM graph with directed edges
## Number of Nodes = 5
## Number of Edges = 6Similarly, edges and nodes can be removed from the graph using the
removeNode and removeEdge methods
respectively. We proceed to remove the flight connection from “DEN” to
“IAH” and subsequently the node “IAH”.
## A graphBAM graph with directed edges
## Number of Nodes = 4
## Number of Edges = 5We can create a subgraph with only the cities “DEN”, “LAX” and “SEA”
using the subGraph method.
## A graphBAM graph with directed edges
## Number of Nodes = 3
## Number of Edges = 3We can extract the from-to relationships
for our graph using the extractFromTo method.
## from to weight
## 1 SEA DEN 259
## 2 SEA LAX 124
## 3 LAX SEA 115The C57BL/6J and C3H/HeJ mouse strains exhibit different
cardiovascular and metabolic phenotypes on the hyperlipidemic
apolipoprotein E(Apoe)
null background. The interaction data for the genes from adipose, brain,
liver and muscle tissue samples from male and female mice were studied.
This interaction data for the various genes is included in the
graph package as a list of data.frames containing
information for from-gene, to-gene and the
strength of interaction weight for each of the tissues
studied.
We proceed to load the data for male and female mice.
We are interested in studying the interaction data for the genes in the brain tissue for male and female mice and hence proceed to represent this data as directed graphs using graphBAM objects for male and female mice.
## from to weight
## 1 10024402938 10024393150 0.835
## 2 10024415240 10024393156 0.667
## 3 10024403128 10024393162 0.312
## 4 10024409968 10024393162 0.482
## 5 10024393260 10024393163 0.997
## 6 10024394731 10024393165 0.714We are interested in pathways that are common to both male and female
graphs for the brain tissue and hence proceed to perform a graph
intersection operation using the graphIntersect method.
Since edges can have different values of the weight attribute, we would
like the result to have the sum of the weight attribute in the male and
female graphs. We pass in sum as the function for handling
weights to the edgeFun argument. The edgeFun
argument should be passed a list of named functions corresponding to the
edge attributes to be handled during the intersection process.
## A graphBAM graph with directed edges
## Number of Nodes = 2117
## Number of Edges = 473If node attributes were present in the graphBAM objects,
a list of named function could be passed as input to the
graphIntersect method for handling them during the
intersection process.
We proceed to remove edges from the graphBAM result we
just calculated with a weight attribute less than a numeric value of 0.8
using the removeEdgesByWeight method.
Once we have narrowed down to the edges that we are interested in, we
would like to change the color attribute for these edges in our original
graphBAM objects for the male and female graphs to “red”.
Before an attribute can be added, we have to set its default value using
the edgedataDefaults method. For our example, we set the
default value for the color attribute to white.
We first obtain the from - to relationship for the resWt
graph using the extractFromTo method and then make use of
the edgeData method to update the “color” edge
attribute.
ftSub <- extractFromTo(resWt)
edgeDataDefaults(male, attr = "color") <- "white"
edgeDataDefaults(female, attr = "color") <- "white"
edgeData(male, from = as.character(ftSub[,"from"]), to = as.character(ftSub[,"to"]), attr = "color") <- "red"
edgeData(female, from = as.character(ftSub[,"from"]), to = as.character(ftSub[,"to"]), attr = "color") <- "red"The MultiGraph class can be used to represent graphs that
share a single node set and have have one or more edge sets, each edge
set representing a different type of interaction between the nodes. An
edgeSet object can be described as representing the
relationship between a set of from-nodes and to-nodes which can either
be directed or undirected. A numeric value (weight) indicates the
strength of interaction between the connected edges.
Self loops are permitted in the MultiGraph class representation (i.e. the from-node is the same as the to-node). The MultiGraph class supports the handling of arbitrary node and edge attributes. These attributes are stored separately from the edge weights to facilitate efficient edge weight computation.
We shall load the graph and RBGL packages that we will be using. We will then create a MultiGraph object and then spend some time examining some of the different functions that can be applied to MultiGraph objects.
We proceed to construct a MultiGraph object with directed
edgeSets to represent the flight connections of airlines
Alaska, Delta, United and American that fly between the cities
Baltimore, Denver, Houston, Los Angeles, Seattle and San Francisco. For
our example, the cities represent the nodes of the MultiGraph
and we have one edgeSet each for the airlines. Each
edgeSet represents the flight connections from an
originating city(from) to the destination
city(to). The weight represents the fare for flying between
the from and to cities.
For each airline, we proceed to create a data.frame containing the originating city, the destination city and the fare.
ft1 <- data.frame(
from = c("SEA", "SFO", "SEA", "LAX", "SEA"),
to = c("SFO", "LAX", "LAX", "SEA", "DEN"),
weight = c( 90, 96, 124, 115, 259),
stringsAsFactors = TRUE)
ft2 <- data.frame(
from = c("SEA", "SFO", "SEA", "LAX", "SEA", "DEN", "SEA", "IAH", "DEN"),
to = c("SFO", "LAX", "LAX", "SEA", "DEN", "IAH", "IAH", "DEN", "BWI"),
weight= c(169, 65, 110, 110, 269, 256, 304, 256, 271),
stringsAsFactors = TRUE)
ft3 <- data.frame(
from = c("SEA", "SFO", "SEA", "LAX", "SEA", "DEN", "SEA", "IAH", "DEN", "BWI"),
to = c("SFO", "LAX", "LAX", "SEA", "DEN", "IAH", "IAH", "DEN", "BWI", "SFO"),
weight = c(237, 65, 156, 139, 281, 161, 282, 265, 298, 244),
stringsAsFactors = TRUE)
ft4 <- data.frame(
from = c("SEA", "SFO", "SEA", "SEA", "DEN", "SEA", "BWI"),
to = c("SFO", "LAX", "LAX", "DEN", "IAH", "IAH", "SFO"),
weight = c(237, 60, 125, 259, 265, 349, 191),
stringsAsFactors = TRUE)These data frames are then passed to MultiGraph class
constructor as a named list, each member of the list being
a data.frame for an airline. A logical vector passed to the
directed argument of the MultiGraph constructor
indicates whether the MultiGraph to be created should have
directed or undirected edge sets.
esets <- list(Alaska = ft1, United = ft2, Delta = ft3, American = ft4)
mg <- MultiGraph(esets, directed = TRUE)
mg## MultiGraph with 6 nodes and 4 edge sets
## edge_set directed edge_count
## Alaska TRUE 5
## United TRUE 9
## Delta TRUE 10
## American TRUE 7The nodes (cities) of the MultiGraph object can be obtained
by using the nodes method.
## [1] "BWI" "DEN" "IAH" "LAX" "SEA" "SFO"To find the fares for all the flights that originate from SEA for the
Delta airline, we can use the mgEdgeData method.
## $`SEA|DEN`
## [1] 281
##
## $`SEA|IAH`
## [1] 282
##
## $`SEA|LAX`
## [1] 156
##
## $`SEA|SFO`
## [1] 237We proceed to add some node attributes to the MultiGraph
using the nodeData method. Before node attributes can be
added, we have to set a default value for each node attribute using the
nodeDataDefuault method. For our example, we would like to
set a default value of square for the node attribute shape.
We would like to set the node attribute “shape” for Seattle to the
value "triangle" and that for the cities that connect with
Seattle to the value "circle".
nodeDataDefaults(mg, attr="shape") <- "square"
nodeData(mg, n = c("SEA", "DEN", "IAH", "LAX", "SFO"), attr = "shape") <-
c("triangle", "circle", "circle", "circle", "circle")The node attribute shape for cities we have not specifically assigned a value (such as BWI) gets assigned the default value of “square”.
## $BWI
## [1] "square"
##
## $DEN
## [1] "circle"
##
## $IAH
## [1] "circle"
##
## $LAX
## [1] "circle"
##
## $SEA
## [1] "triangle"
##
## $SFO
## [1] "circle"We then update the edge attribute color for the Delta
airline flights that connect with Seattle to “green”. For the remaining
Delta flights that connect to other destination in the MultiGraph, we
would like to assign a default color of “red”.
Before edge attributes can be added to the MultiGraph, their default
values must be set using the mgEdgeDataDefaults method.
Subsequently, the megEdgeData<- method can be used to
update specific edge attributes.
mgEdgeDataDefaults(mg, "Delta", attr = "color") <- "red"
mgEdgeData(mg, "Delta", from = c("SEA", "SEA", "SEA", "SEA"),
to = c("DEN", "IAH", "LAX", "SFO"), attr = "color") <- "green"
mgEdgeData(mg, "Delta", attr = "color")## $`DEN|BWI`
## [1] "red"
##
## $`IAH|DEN`
## [1] "red"
##
## $`SEA|DEN`
## [1] "green"
##
## $`DEN|IAH`
## [1] "red"
##
## $`SEA|IAH`
## [1] "green"
##
## $`SEA|LAX`
## [1] "green"
##
## $`SFO|LAX`
## [1] "red"
##
## $`LAX|SEA`
## [1] "red"
##
## $`BWI|SFO`
## [1] "red"
##
## $`SEA|SFO`
## [1] "green"We are only interested in studying the fares for the airlines Alaska,
United and Delta and hence would like to create a smaller
MultiGraph object containing edge sets for only these airlines.
This can be achieved using the subsetEdgeSets method.
We proceed to find out the lowest fares for Alaska, United and Delta
along the routes common to them. To do this, we make use of the
edgeSetIntersect0 method which computes the intersection of
all the edgesets in a MultiGraph. While computing the intersection of
edge sets, we are interesting in retaining the lowest fares in cases
where different airlines flying along a route have different fares. To
do this, we pass in a named list containing the weight
function that calculates the minimum of the fares as the input to the
edgeSetIntersect0 method. (The user has the option of
specifying any function for appropriate handling of edge attributes
).
## MultiGraph with 6 nodes and 1 edge sets
## edge_set directed edge_count
## Alaska_United_Delta TRUE 5The edge set by the edgeSetIntersect0 operation is named
by concatenating the names of the edgeSets passed as input to the
function.
## $`SEA|DEN`
## [1] 259
##
## $`SEA|LAX`
## [1] 110
##
## $`SFO|LAX`
## [1] 65
##
## $`LAX|SEA`
## [1] 110
##
## $`SEA|SFO`
## [1] 90The C57BL/6J and C3H/HeJ mouse strains exhibit different
cardiovascular and metabolic phenotypes on the hyperlipidemic
apolipoprotein E(Apoe)
null background. The interaction data for the genes from adipose, brain,
liver and muscle tissue samples from male and female mice were studied.
This interaction data for the various genes is included in the
graph package as a list of data.frames containing
information for from-gene, to-gene and the
strength of interaction weight for each of the tissues
studied.
We proceed to load the data for male and female mice.
## [1] "adipose" "brain" "liver" "muscle"## from to weight
## 1 10024404688 10024393150 0.853
## 2 10024406215 10024393156 0.513
## 3 10024411796 10024393163 1.000
## 4 10024415608 10024393167 0.727
## 5 10024399302 10024393196 0.342
## 6 10024399912 10024393196 0.555The esetsFemale and esetsMale objects are a
named list of data frames corresponding to the data
obtained from adipose, brain, liver and muscle tissues for the male and
female mice that were studied. Each data frame has a from, to and a
weight column corresponding to the from and to genes that were studied
and weight representing the strength of interaction of the corresponding
genes.
We proceed to create MultiGraph objects for the male and female data sets by making use of the MultiGraph constructor, which directly accepts a named list of data frames as the input and returns a MultiGraph with edgeSets corresponding to the names of the data frames.
female <- MultiGraph(edgeSets = esetsFemale, directed = TRUE)
male <- MultiGraph(edgeSets = esetsMale, directed = TRUE )
male ## MultiGraph with 7081 nodes and 4 edge sets
## edge_set directed edge_count
## adipose TRUE 1601
## brain TRUE 2749
## liver TRUE 3690
## muscle TRUE 3000## MultiGraph with 7072 nodes and 4 edge sets
## edge_set directed edge_count
## adipose TRUE 2108
## brain TRUE 2789
## liver TRUE 3584
## muscle TRUE 2777We then select a particular gene of interest in this network and proceed to identify its neighboring genes connected to this gene in terms of the maximum sum of weights along the path that connects the genes for the brain edge set.
We are interested in the gene “10024416717” and the sum of the
weights along the path that connects this genes to the other genes for
the brain tissue. Since the algorithms in the RBGL package
that we will use to find the edges that are connected to the gene
“10024416717” do not work directly with MultiGraph objects, we
proceed to create graphBAM objects from the male and female
edge sets for the brain tissue.
MultiGraph objects can be converted to a named list of
graphBAM objects using the graphBAM
method.
## A graphBAM graph with directed edges
## Number of Nodes = 7081
## Number of Edges = 2749We then identify the genes connected to gene “10024416717” as well as
the sum of the weights along the path that connect the identified genes
using the function bellman.ford.sp function from the RBGL
package.
maleWt <- bellman.ford.sp(maleBrain, start = c("10024416717"))$distance
maleWt <- maleWt[maleWt != Inf & maleWt !=0]
maleWt## 10024409301 10024409745
## 0.636 1.389femaleWt <- bellman.ford.sp(femaleBrain, start = c("10024416717"))$distance
femaleWt <- femaleWt[femaleWt != Inf & femaleWt != 0]
femaleWt## 10024393904 10024409503
## 0.789 0.866For the subset of genes we identified, we proceed to add node
attributes to our original MultiGraph objects for the male
and female data. The node “10024416717” and all its connected nodes are
assigned a color attribute “red” while the rest of the nodes are
assigned a color attribute of “gray”.
nodeDataDefaults(male, attr = "color") <- "gray"
nodeData(male , n = c("10024416717", names(maleWt)), attr = "color") <- c("red")
nodeDataDefaults(female, attr = "color") <- "gray"
nodeData(female, n = c("10024416717", names(femaleWt)), attr = "color" ) <- c("red")Our MultiGraph objects now contain the required node
attributes for the subset of genes that we have narrowed our selection
to.
For the MultiGraph objects for male and female, we are
also interested in the genes that are common to both
MultiGraphs. This can be calculated using the
graphIntersect method.
## MultiGraph with 5699 nodes and 4 edge sets
## edge_set directed edge_count
## adipose TRUE 88
## brain TRUE 473
## liver TRUE 455
## muscle TRUE 370The operations we have dealt with so far only deal with manipulation of MultiGraph objects. Additional functions will need to be implemented for the visualization of the MultiGraph objects.