(2) Let M be a linear module consisting of the chain \(v_1, \ldots , v_k\). It is use this link known that any rooted tree with

k

{\displaystyle k}

leaves has at most

k

1

{\displaystyle k-1}

internal nodes.
A module of a graph is a generalization of a connected component. From the table, we can see that the index sizes of \(G_c\) are smaller for almost every graph than \(G^\epsilon \) for all of the four algorithms, although for the arXiv, PubMed, Citeseerx and Patent datasets the difference is very small and for PubMed the index size of Feline is smaller in \(G^\epsilon \) than in \(G_c\) as well.

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Nodes in the network are not necessarily equivalent, as usually not all of the corresponding proteins have also been tested as baits in the underlying experiments. Although the module representation can be helpful to derive hypotheses from interaction networks, interpretation requires particular attention for experimental datasets. Over the last decades, the problem has been extensively studied and many advanced algorithms have been proposed, with most of them relying on building smart indexes that can strike a balance between online query processing time and offline index construction time (and index size). 2. A subsystem makes a convenient package to hand off to a team or a subcontractor to implement.

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Note that LCA(u, v) corresponds either to a module in some compressed graph \(G_i\)\((i\in [1, c-1])\), or to the final compressed graph \(G_c\) (i. A subsystem can be pretty much anything you want it to be, but it often describes a part of a system you can look here (1) carries out a functionally cohesive subset of the overall systems mission, (2) can be executed independently, and (3) can be developed and deployed incrementally. CSCIs are selected based on trade-offs among software function, size, host or target computers, developer, support concept, plans for reuse, criticality, interface considerations, the need to be separately documented and controlled, and other factors. Here, the added proteins are not baits and therefore parallel modules are alternative, but not necessarily exclusive alternatives. cpp - file. See the GNU General Public License for more details.

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[12] uses the concept of chain cover to improve two-hop and proposes a three-hop labeling that creates a transitive closure contour (Con(G)) of graph G using chain decomposition, and then applies two-hop techniques. By definition, M is an independent set, and all the vertices have the same external ancestors and the same external descendants. The following examples illustrate how modular decomposition can reveal the combinatorial assembly of complexes from interaction networks. A connected component has the property that it is a set [math]\displaystyle{ X }[/math] of vertices such that every member of [math]\displaystyle{ X }[/math] is a non-neighbor of every vertex not in [math]\displaystyle{ X }[/math]. Modular decomposition of the experimental TAP network characterizes the existence of complex variants (Figure 6).

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Some proteins are specific to individual NFκB members. Also as observed in [22], if G has no redundant edges, then all vertices in an equivalence class form an independent set, that is, there are no edges between the vertices in the same equivalence class.

{\displaystyle R_{1}\times \cdots \times R_{n}. Given a pointer to a node, this structure could return the set of vertices of

G

{\displaystyle G}

that it represents in

O

find
(
k
)

{\displaystyle {\mathcal {O}}(k)}

time. .

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