An efficient algorithm for enumerating all possible input nodes in controlling complex networks

Controlling complex networks is of great importance in many application regions. Recent works found that the minimum number of input nodes (MIS) used to control a network can be obtained by the maximum matching. However, the maximum matchings of a network are not unique, and there may exist numerous MISs. Finding all possible input nodes is difficult for the large-scale networks because of high computational costs. Here we present an efficient algorithm to enumerating all possible input nodes of a network. We rigorously prove that all possible input nodes can be obtained by a simple modification of the maximum matching algorithm, which allows us to obtain all possible input nodes (the union of all MISs) by only computing one MIS. The experiment results on both synthetic and real networks show that the computational complexity of the proposed algorithm is significantly improved contrast to the previous one. Speedup of up 100000x compared with the previous algorithm was observed for large-scale synthetic networks and real networks.

[1]  Jure Leskovec,et al.  The dynamics of viral marketing , 2005, EC '06.

[2]  Ian T. Foster,et al.  Mapping the Gnutella Network: Properties of Large-Scale Peer-to-Peer Systems and Implications for System Design , 2002, ArXiv.

[3]  J. Montoya,et al.  Small world patterns in food webs. , 2002, Journal of theoretical biology.

[4]  D. Baird,et al.  Assessment of spatial and temporal variability in ecosystem attributes of the St Marks national wildlife refuge, Apalachee bay, Florida , 1998 .

[5]  Richard M. Karp,et al.  A n^5/2 Algorithm for Maximum Matchings in Bipartite Graphs , 1971, SWAT.

[6]  Tore Opsahl,et al.  Clustering in weighted networks , 2009, Soc. Networks.

[7]  Kazuo Murota,et al.  Matrices and Matroids for Systems Analysis , 2000 .

[8]  Mathieu Bastian,et al.  Gephi: An Open Source Software for Exploring and Manipulating Networks , 2009, ICWSM.

[9]  Derek Ruths,et al.  Control Profiles of Complex Networks , 2014, Science.

[10]  Richard M. Karp,et al.  A n^5/2 Algorithm for Maximum Matchings in Bipartite Graphs , 1971, SWAT.

[11]  Stanford,et al.  Learning to Discover Social Circles in Ego Networks , 2012 .

[12]  R. Kálmán.  Mathematical description of linear dynamical systems , 1963 .

[13]  A. Vinayagam,et al.  A Directed Protein Interaction Network for Investigating Intracellular Signal Transduction , 2011, Science Signaling.

[14]  S. Shen-Orr,et al.  Network motifs in the transcriptional regulation network of Escherichia coli , 2002, Nature Genetics.

[15]  K. Sneppen,et al.  Specificity and Stability in Topology of Protein Networks , 2002, Science.

[16]  Stefan Wuchty,et al.  Controllability in protein interaction networks , 2014, Proceedings of the National Academy of Sciences.

[17]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[18]  F. Fairman.  Introduction to dynamic systems: Theory, models and applications , 1979, Proceedings of the IEEE.

[19]  R. Tsien,et al.  Specificity and Stability in Topology of Protein Networks , 2022 .

[20]  H. Kuhn.  The Hungarian method for the assignment problem , 1955 .

[21]  Ginestra Bianconi,et al.  Network controllability is determined by the density of low in-degree and out-degree nodes. , 2014, Physical review letters.

[22]  Sarah Theiss,et al.  Introduction To Dynamic Systems Theory Models And Applications , 2016 .

[23]  Arvind Kumar,et al.  Challenges of understanding brain function by selective modulation of neuronal subpopulations , 2013, Trends in Neurosciences.

[24]  M. De Domenico,et al.  The Anatomy of a Scientific Rumor , 2013, Scientific Reports.

[25]  Lenka Zdeborová,et al.  The number of matchings in random graphs , 2006, ArXiv.

[26]  Vladimir Batagelj,et al.  Exploratory Social Network Analysis with Pajek , 2005 .

[27]  Albert-László Barabási,et al.  Control of fluxes in metabolic networks , 2016, Genome research.

[28]  Jure Leskovec,et al.  Predicting positive and negative links in online social networks , 2010, WWW '10.

[29]  Endre Csóka,et al.  Emergence of bimodality in controlling complex networks , 2013, Nature Communications.

[30]  Albert-László Barabási,et al.  Controllability of complex networks , 2011, Nature.

[31]  Bethany S. Dohleman.  Exploratory social network analysis with Pajek , 2006 .

[32]  C Berge,et al.  TWO THEOREMS IN GRAPH THEORY. , 1957, Proceedings of the National Academy of Sciences of the United States of America.

[33]  V. Sunitha,et al.  Identification of critical regulatory genes in cancer signaling network using controllability analysis , 2017 .

[34]  A. Barabasi,et al.  Controllability analysis of the directed human protein interaction network identifies disease genes and drug targets , 2015, Proceedings of the National Academy of Sciences.

[35]  Tao Jia,et al.  Control Capacity and A Random Sampling Method in Exploring Controllability of Complex Networks , 2013, Scientific Reports.

[36]  Yuanyuan Pu,et al.  Input graph: the hidden geometry in controlling complex networks , 2016, Scientific Reports.

[37]  F. Stokman,et al.  Evolution of sociology freshmen into a friendship network , 2003 .

[38]  Jure Leskovec,et al.  Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters , 2008, Internet Math..

[39]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[40]  Christos Faloutsos,et al.  Graphs over time: densification laws, shrinking diameters and possible explanations , 2005, KDD '05.

[41]  Guido Caldarelli,et al.  Evolution of Controllability in Interbank Networks , 2013, Scientific Reports.

[42]  L. Aravind,et al.  Comprehensive analysis of combinatorial regulation using the transcriptional regulatory network of yeast. , 2006, Journal of molecular biology.